We know that the universe is not vacuum. The average temperature of the universe is 3° above absolute zero. So some "aether" really exists, but that is not some gas with very low density, but stardust. (I know that aether was only concept for spreading of light in medium, but aether wind should exist.) So why we don't calculate with aether wind?
I am intrigued by your question and take it to be roughly:
there's stuff out there, so how do we know the true value of $c$ isn't "hidden" from us by this stuff: i.e. would $c$ be different if that stuff weren't there and how do we know $c$ isn't affected by this "stuff"?
The answer is that the most striking and important feature about measurement-of-$c$ experiments is not the value of $c$ that they yield, but the way $c$ transforms between inertial observers.
As I talk about in detail here, here, here and here, if we make basic homogeneity and symmetry assumptions about the universe, then we can derive all possible relativities: a whole family of them, each family member characterised by a universal constant $c$ which has the outstanding and defining property that its value is the same for all observers, and Galilean relativity is the special limiting case as $c\to\infty$.
Once we have observed a speed with this property, this is powerful experimental evidence that our symmetry and homogeneity assumptions hold true. In other words, whatever "stuff" there may be out there, and whatever it is we observe to have this invariant $c$, be it a photon, a neutrino (almost) or a massless pink aardvark, we know that it (1) must be massless and (2) cannot be having any interaction with whatever "stuff" might be moving relative to us, because such interactions would violate the basic homogeneity and symmetry assumptions that beget the invariant $c$ in the first place. Thus, for example, because we can do a negative-result Michelson-Morley experiment here on Earth, we know that there is no optical medium: i.e. no hidden "stuff" (dark matter) that is skewing our results unless this hidden matter has no interaction with light.
You are talking of the dust/atoms between galaxies and galactic clusters and they are taken in consideration when calculations are made about luminosities etc. After all that is the way we know there exists matter in space, by the variations in expected luminosities.
Here is a reference with references to the various estimates of the density of atoms in space. Mostly less than 1 atom per cubic centimeter. Not enough to create a wind, which is an emergent phase in much higher density matter.
Many experiments such as the Michelson-Morley Experiment proved that if the "aether wind" exists it is extremely small and orders of magnitude less than it should be based on a classical aether theory.
The concept of an "aether" in fully MODERN terms in not dead. This aether would be a block universe fully 4D aether or a 3D LET type aether evolving through time. User36375 is right that on some levels modern physicists think there is an aether but again this has almost nothing in common with the classical idea.
Nothing is wrong with SR's formal derivation as it assumes consistency of the speed of light and derives such items like the Doppler Shift. It works very well in practice.
Nothing is wrong with neo-LET's derivation of all the equations of relativity either. For example the classical Doppler Shift equations are:
fms = f/(1+v/c) and fmo = f (1-v/c)
LET has time dilation and it uses the Einstein light clock which has a moving frame slowing down in time by b = (1-(v/c)^2)^.5. It applies time dilation asymmetrically as shown below:
A moving frame moves slower through time so its frequency emitted is lower.
fms = f b / (1+v/c)
Stationary frame moves faster through time so its frequency emitted is higher.
fmo = f (1-v/c)/b
fms = fmo = (1+v/c)^.5/(1-v/c)^.5 and likewise kmo = kms where k is the wavenumber.
ALL observables between reference frames are the SAME. E = h f and p = h k. M-M tried to show that kmo =/= kms (or equivalently wlmo =/= wlms). As far as any observer is concerned in either reference they both can claim to be the stationary observer OR the moving observer (a little known fact about SR is an observer can always claim they are the one moving and the other guy is stationary). I personally don't think this is a coincidence and using this same line of reasoning ALL of SR can be derived and expanded to all reference frames. Even Minkowski math and GR (as an acceptable approximation) can follow this line of reasoning.
This matches SR exactly yet two different mechanism occur. They're externally symmetric and the transverse forms (which Lorentz had trouble with early on) also are the same. SR can incorporate a preferred frame but no preferred frame needs to be referenced so we don't need one in the math. Nothing is ad hoc about this. You can start with one reference frame assume ALL particles not bound by a field (like the Higgs etc) move at c. This is just a standard old fashion medium idea EXCEPT the particles are all waves/wave packets themselves. Waves don't push through their medium they propagate. The Couder Walking Drop Experiment and ordinary quantum solids and liquids exhibit relativistic behaviors. The drops length contract and quantum systems exhibit relativistic behaviors even though they have a medium. They do this because the waves and the drop aren't like classical objects pushing through the medium. Rather they are part of the medium themselves. In fact classical motion might be an illusion replaced with propagation.
According to Quantum Field Theory (the most accurate theory known) particles are excitations of fields existing throughout space. Whether these fields are a three dimensional medium evolving through time or a fully four dimensional medium is not known. In fact with the math I showed here for all v < c (everything we can test) they are the same thing (although some LET like aether theories propose differences so they can run scientific tests NOT because they are necessary).
Classical aethers fight the Doppler Shift like something is pushing through it in a classical way like a boat through water. Lets derive the Lorentz Transform using the Doppler Shift equation I have. Lets pick a frequency Doppler Shift:
fmo = f (1-v/c)/b
Now lets say that for a give frequency f constant = observed time in the other frame. That is j f = t. This is just a light clock idea that any physicist would agree with. Look here under the Doppler Shift section: https://en.wikipedia.org/wiki/Twin_paradox.
tmo/j = t/j (1 - v/c)/b
tmo = t (1 - v/c)/b = (t - v/c t)/b let's synchronize clocks for the comoving term using c t = x or t = x/c to put it in the conventional form. Einstein also uses light to synchronize clocks (there's a reason for this that I could derive also).
tmo = (t - v/c x/c)/b = (t- v x/c^2)/b = Lorentz t Transform
tmo = tms because what we started with was equal. This incorporates all of relativity's length contraction, time dilation, and simultaneity. Notice, however, that while the observables between frames are symmetric here the reference frames are asymmetric. tmo and tms have different underlying mechanisms. However, uniform changes within a reference frame can't be detected, only observables between reference frames.
Neither neo-LET (the modern verision of LET) nor SR need to have any "aether drag." In fact I'd go far enough to say that LET only make sense if everything is wavelike (which it is according to QFT and QM). SR seems to require it also. The natural result of everything being a propagation of the same medium is relativity. Whether this medium is fully 4D or 3D evolving (but appearing 4D to internal observers) isn't known.
In either case I don't foresee any aether drag being necessary or Lorentz invariance violation. These may occur but only at insanely high energies. GR is upheld also for all but perhaps the most extreme curvatures (like inside a blackhole which we known nothing about anyways). I have many more equations but for the sake of room I'm not including it here. I like LET because it seems to force a fully wave like explanation that matches QFT explanation. SR matches LET exactly so it merges with QFT well for all but the most extreme energies (or frequencies) but GR is not fully wavelike and it does not fully match LET. Pretty close but its hard to reconcile it with GR under the most extreme conditions. But GR is expected to need modification there anyways. In any case reality is relativistic, no aether drag is needed.
The "aether wind" was supposed to be the Earth's motion through an absolutely stationary space. The aether is not an absolutely stationary space. The aether is displaced by the particles of matter which exist in it and move through it.
"The word 'ether' has extremely negative connotations in theoretical physics because of its past association with opposition to relativity. This is unfortunate because, stripped of these connotations, it rather nicely captures the way most physicists actually think about the vacuum. . . . Relativity actually says nothing about the existence or nonexistence of matter pervading the universe, only that any such matter must have relativistic symmetry. [..] It turns out that such matter exists. About the time relativity was becoming accepted, studies of radioactivity began showing that the empty vacuum of space had spectroscopic structure similar to that of ordinary quantum solids and fluids. Subsequent studies with large particle accelerators have now led us to understand that space is more like a piece of window glass than ideal Newtonian emptiness. It is filled with 'stuff' that is normally transparent but can be made visible by hitting it sufficiently hard to knock out a part. The modern concept of the vacuum of space, confirmed every day by experiment, is a relativistic ether. But we do not call it this because it is taboo."
- Robert B. Laughlin, Nobel Laureate in Physics, endowed chair in physics, Stanford University
"any particle, even isolated, has to be imagined as in continuous “energetic contact” with a hidden medium ... If a hidden sub-quantum medium is assumed, knowledge of its nature would seem desirable. It certainly is of quite complex character. It could not serve as a universal reference medium, as this would be contrary to relativity theory."
- Louis de Broglie, Nobel Laureate in Physics
"According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense."
- Albert Einstein, Nobel Laureate in Physics
The relativistic ether referred to by Laughlin is the hidden sub-quantum medium referred to by de Broglie is the ether which propagates light referred to by Einstein.
'Galactic Pile-Up May Point to Mysterious New Dark Force in the Universe' http://www.wired.com/wiredscience/2013/01/musket-ball-dark-force/
"The reason this is strange is that dark matter is thought to barely interact with itself. The dark matter should just coast through itself and move at the same speed as the hardly interacting galaxies. Instead, it looks like the dark matter is crashing into something — perhaps itself – and slowing down faster than the galaxies are. But this would require the dark matter to be able to interact with itself in a completely new an unexpected way, a “dark force” that affects only dark matter."
- quote from paper cited above
It's not a new force. It's the aether displaced by each of the galaxy clusters interacting analogous to the bow waves of two boats which pass by each other.
'The Milky Way's dark matter halo appears to be lopsided'
The Milky Way's 'dark matter halo' is lopsided due to the matter in the Milky Way moving through and displacing the aether.
'Offset between dark matter and ordinary matter: evidence from a sample of 38 lensing clusters of galaxies' http://arxiv.org/PS_cache/arxiv/pdf/1004/1004.1475v1.pdf
"Our data strongly support the idea that the gravitational potential in clusters is mainly due to a non-baryonic fluid, and any exotic field in gravitational theory must resemble that of CDM fields very closely."
- quote from paper cited above
The offset is due to the galaxy clusters moving through the aether. The analogy is a submarine moving through the water. You are under water. Two miles away from you are many lights. Moving between you and the lights one mile away is a submarine. The submarine displaces the water. The state of displacement of the water causes the center of the lensing of the light propagating through the water to be offset from the center of the submarine itself. The offset between the center of the lensing of the light propagating through the water displaced by the submarine and the center of the submarine itself is going to remain the same as the submarine moves through the water. The submarine continually displaces different regions of the water. The state of the water connected to and neighboring the submarine remains the same as the submarine moves through the water even though it is not the same water the submarine continually displaces. This is what is occurring as the galaxy clusters move through and displace the aether.
What we have detected is the state of the aether as determined by its connections with the matter and the state of the aether in neighboring places, which is the state of displacement of the aether.