Did Ole Rømer measure the one-way speed of light or the two-way speed of light? Simple question really. I'm having a convo with someone on Twitter who is a fan of the "Anisotropic Synchrony Convention" by dr. Lisle. It's a link to Answers in Genesis, so you know it's good (for a certain value of good).
Anyway, I have countered that Ole Rømer's observations (and of course the observations since, with improved accuracy), constitute a measurement of the one-way speed of light. My opponent on Twitter believes that Rømer measured the two-way speed of light.
Does that make the Einstein synchronization convention more plausible, or is Einstein's synchronization convention just more convenient?
That was the question. What follows is some more background info, and maybe something else to discuss. Should I create separate questions for the following?
I have also countered that the LIGO - Virgo detection of gravitational waves produced by colliding neutron stars constitutes a direct measurement of c (close to c) as these observatories work in unison.

"Though the LIGO detectors first picked up the gravitational wave in
the United States, Virgo, in Italy, played a key role in the story.
Due to its orientation with respect to the source at the time of
detection, Virgo recovered a small signal; combined with the signal
sizes and timing in the LIGO detectors, this allowed scientists to
precisely triangulate the position in the sky. After performing a
thorough vetting to make sure the signals were not an artifact of
instrumentation, scientists concluded that a gravitational wave came
from a relatively small patch in the southern sky."

I have also countered that GPS signals provide a measurement of the one-way speed of light as the signals of the various satellites must be close to c for the receiver to be able to calculate the position on the globe.
At any rate, I have read the different questions asked here about the Veritasium video, and, in fact, my opponent on Twitter has linked me to it and also to this forum. To be exact, to this question.
Lastly, I am going to propose a way to measure the one-way speed of light. It requires one emitter and two receivers some distance away from each other and from the emitter in a straight line.
Step one: The emitter fires a laser beam onto a mirror in its path. The mirror reflects the light to a secondary mirror which reflects it towards both receivers, starting their clocks at the same time.
Step two: The mirror gets removed from the path of the laser.
Step three: The emitter fires a second laser beam towards both receivers. One receiver gets half of the laser beam, stopping its clock, the second receiver gets the other half to stop its clock.
We know the distance between the two receivers, and we have measured the time it took for the light to travel between the two receivers.
Would that experimental setup be conclusive?
Edit
I've simplified the setup of the experiment and added a drawing.

t0: E1 emits light in all directions.
t1: This synchronizes the clocks on detectors D1 and D2.
t2: After synchronization, E2 emits a laser beam towards both detectors.
t3: D1 detects the light first and stops its timer.
t4: D2 detects the light second and stops its timer.
One-way speed of light: c = L / (t4-t3)
 A: The Einstein synchronization convention really is just a convention. Nothing prevents you from synchronizing clocks in some other way. Einstein synchronization just happens to usually be more convenient than alternatives when it's possible (which it isn't always).
Lisle's paper effectively defines a time coordinate $t' = t + (1{-}ε)|x|/c$ for some small $ε>0$. With respect to this time coordinate, the speed of light moving toward the origin (i.e. the Earth) is $-dx/dt' = c/ε \gg c$.
You can't falsify this because it's just a mathematical substitution of variables. It's not clear to me what setup you intend for your one-way speed of light measurement, but whatever it is, you can do the exercise of assigning standard inertial spacetime coordinates to every event in the problem, then calculating $t'$ for each event, and then describing in words what this "means". You'll find that everything conspires to give you a result consistent with an isotropic speed of light, even though the speed is "really" anisotropic. You can also "explain" GPS signals, Rømer's experiment, or anything else in Lisle's coordinates. This proves nothing except the internal consistency of algebra and calculus.
Lisle claims that God used that convention to synchronize the biblical creation: in other words, that the universe began on the surface $t'=t_0\approx -6000\text{ yr}$. That's an actual physical claim that I suppose is falsifiable in principle. But the synchronization conventions that we (as opposed to God) use have no physical significance. There's no evidence that anything in nature ever depends on whether events are simultaneous by any convention at all.
Here's an answer I wrote about the Veritasium video. Summary: it's worse than Lisle's paper, because at least Lisle's paper makes a claim that's falsifiable in principle.
A: First an unimportant detail: Ole Rømer described the assessment of the speed of light that he is rightly remembered for, but to my knowledge he wasn't actually in the position to obtain measurements that were accurate enough.
Correction in response to a comment: I misremembered.
Rømer's ideas and results were known to his contemporaries through correspondence. It was just that these ideas were not formally published.

Before I proceed there is a essential point I need to discuss. Some people regard the question of whether a one-way measurement of the speed of light is possible in connection with questioning whether it is possible to set up an experimentum crucis to distinguish between a Lorentz aether theory on one hand or special relativit on the other hand. My expectection is that no such experiment is possible. That is: I expect any one-way measurement of the velocity of light to find the same value as a two-way measurement.
I concur:
If it is granted that we expect the moons of other planets to move according to the the laws of motion then the shift in the timing can be attributed to different time transit delay depending on travel distance. We know the distances between the planets in the solar system. Putting al that together the speed of light can be inferred.
The only criticism one can level against that is that it is a process with several stages of inferring.
Then again, multiple stages of inferring is how the majority of measurements are obtained. (Example: distances to other galaxies. Distances to nearby Cepheids are assessed by parallax measurement. Distant Cepheids are identifed and the distance is inferred from the measured luminosity.)

A two-way measurement of the speed of light requires far less stages of inferring, if any.
The intellectual challenge is the issue whether it is possible to perform a one-way measurement of the speed of light with a setup that is just as simple as a setup for a two-way measurement of light.

About time-keeping on Earth in general:
There are multiple centers for time-keeping around the world, and they work together to provide the world with a coordinated world time.
Having a high precision coordinated world time is crucially important for astronomy. There are forms of radio astronomy where each observatory records data with time labeling at the highest possible level. Disk drives containing these data are from over the world shipped to a central facility. In this facility the data are processed, and because of the high precision of time labeling they can correlate the signal phase. Thus data from distant observatories can be processed as if those observatories are at oppposite ends of the perimeter of a planet sized radio receiver dish.
Now comes the important part:
The way world coordinated time is maintained is not by Einstein synchronization. For this specific application Einstein synchronization would not work.
To explain why it wouldn't work I will describe a highly stylized version of how world time coordination is done; the underlying principle is the same.
Image a number of time centers located at equal intervals along the equator. Let me make that (arbitrary choice) 12 centers.
To maintain synchronized time they are continuously relaying time signals, both in clockwise direction and in counterclockwise direction.
Let me say that 12 signals are relaying in each directions. Each signal is a pulse, with an identifyer.
The procedure is that on each relay step there is an option to make a minimal adjustment such that the time spacing between the 12 clockwise propagating pulses is as close to equal as possible, and that the time between the 12 counterclockwise propagatign pulses is as close to equal as possible.
If the Earth would not be rotating then the counter-propatating trains of pulses would behave the same.
On our rotating Earth the rotation introduces a bias. The pulses traveling from west to east take a bit longer to make it from station to station. Conversely, the pulses traveling from east to west take less time.

The animation depicts the phenomenon. In interferometry this phenomenon is called 'the Sagnac effect'. One particular form of interferometery, ring laser interferometry, uses the Sagnac effect to measure the Earth rotation rate (and minute variations of it).
The underlying principle of the Sagnac effect is that the speed of light is the same in all directions.
The blue and red dots represent counterpropagating pulses. The counterpropagating pulses have the same speed everywhere. Note that in the animation they cross each other at the same spot all the time, because they are propagating at the same speed.
The four grey dots represent relay stations along the way.
The operators of the relay stations know the rotation rate of the system. The operators know how much time interval to expect between the blue pulses and the red pulses. Even if the operators would not know in advance what the rotation rate of the system is, they can infer that rotation rate from the difference in travel time between the blue and red pulses.

What would happen with Einstein synchronization
Applying Einstein synchronization would fail to meet the demands:
The 12 stations would have to pair up. 1-2, 2-3, 3-4 ... 11-12 etc. They can do all those pair-wise synchronizations, with application of Einstein synchronisation. Except: then you cannot close the loop. If all pairs have applied Einstein synchronization then for the pair 12-1 there will be a time gap.
For world coordinated time such a gap is unacceptable. The procedure to maintain world coordinated time must take the Earth's rotation into account, so that is what happens.
On the real Earth the time keeping centers are not equally spaced of course, so that has to be taken into account. Also, they are at different elevation above sea level, hence at different geopotential height which gives rise to difference in gravitational time dilation effect, which has to be taken into account. Clearly there are a lot of difficulties; evidently the engineers have overcome all of them.

GPS
The precise time-keeping that enables worldwide consistent GPS is dependent on having a single coordinated world time.
Also, given that a single coordinated world time is used, and given that the Earth is rotating: depending on where a GPS satellite is relative to the GPS receiver the signal may be traveling east-to-west or west-to-east. For west-to-east travel you expect more travel time than for east-to-west travel. The GPS technology takes this difference into account.
A: This second answer is specifically for the setup represented with the diagram in the question.

E1, E2, D1 and D2 are co-moving with each other.
The triangle E1, D1, D2 is of course intended as an equilateral triangle.
As we know: when the propagation of light is represented in a coordinate system that is co-moving with this setup then light emitted from E1 in effect defines simultaneity for that coordinate system. In terms of co-moving representation: light emitted from E1 reaches D1 and D2 simultaneously.

The same proceedings can with equal validity be represented in any coordinate system of the overall equivalence class of inertial coordinate systems.
When represented in any coordinate system not co-moving with this setup the plane of simultaneity comes out differently.
Generalizing:
In all cases where the representation can with equal validity be represented in terms of any member of the equivalence class of inertial coordinate systems: relativity of simultaneity is inescapable.

That is to say: the question of whether one-way measurement of the speed of light is possible is regarded as interconnected with the question of whether there is any way to avoid relativity of simultaneity.
Any setup that does not eliminate relativity of simultaneity is regarded as not being a one-way measurement of the speed of light.
A: Regarding your proposed experiment: it seems to me that you have already assumed that light travels with the same speed in any direction when you synchronize the clocks of D1 and D2 in the way you propose. If the one-way speed of light is not isotropic, then it would take different amounts of time for the beam to travel the distance E1-D1 compared to  E1-D2, and the clocks of D1 and D2 would then not be synchronized in the way that I think you want.
