Do photons slow down? If $c$ is the 2-way speed of light and we can't measure the one-way speed, how do we know with absolute certainty that photons don't loose speed after a first bounce off of a reflective surface? If we don't know for sure, can we say with certainty that those photons that were emitted were moving at the same speed as those bouncing off of the surface?
 A: We can compare the there-and-back speed to the speed along a polygonal path.
Using any of these models


*

*The light loses the same fraction of speed on each bounce

*The light loses the same amount of speed on each bounce

*The light slows down only on the first bounce (no idea why, but let's run with it)
the measured polygonal path speed would be slower than the there-and-back speed.

And there are several classes of interferometers that use polygonal light paths, so the experiment is done as a side effect on a regular basis.
A: The equations that govern light reflection from a surface are classical electrodynamics, or if you want to be really serious about this quantum electrodynamics. Both of these are time symmetric i.e. if we exchange $t$ for $-t$ the equations still correctly describe the time evolution. This symmetry is called T-Symmetry.
But if the light slowed down after the first bounce this would introduce a time asymmetry because if we reverse the time direction we would get a light ray that increased its speed after the first bounce. If such a gross time asymmetry existed it would mean both classical and quantum electrodynamics would fail spectacularly, and such failures would be immediately detectable in experiments. Our failure to detect a violation of T-symmetry suggests that light cannot change speed on reflection.
As it happens there are very, very small violations of T-symmetry, and we have recently managed to find experimental evidence for them. However these violations are associated with the weak force not the electromagnetic force and they have no bearing on the speed of light.
A: In short, we can't. Any measurement of the speed of light in which light only travels in one direction requires synchronizing clocks at the source and destination. Any synchronization scheme necessarily assumes that the speed of light is the same in both directions (due to time dilation effects from moving the clocks apart), so no measurement can actually be done without assuming the conclusion. All we know is that the average speed of a light beam on a round trip is equal to the speed of light. Here's a Wikipedia article on the issue.
However, a universe in which light traveled faster in one direction than another seems extremely strange. The universe doesn't look different in one direction than another, but light would travel faster in one direction in a completely unobservable way. This sort of mystery would border on a cosmic conspiracy to hide the universe's preferred direction of travel.
Since assuming light travels the same speed in all directions allows us to make very accurate predictions about the behavior of the universe and a lot of things in it, scientists feel comfortable making that assumption. If light did travel at different speeds in different directions, relativity seems to perfectly hide this fact from us, so it doesn't seem to really matter anyway.
A: 
Do photons slow down?

Yes, a photon moving downwards slows down. If it reflects off a mirror on the floor and then moves upwards, it speeds up. Not many people know this, but it is true. See Is The Speed of Light Everywhere the Same? written by Don Koks, the PhysicFAQ editor. Also see the Einstein digital papers. Einstein said "a curvature of rays of light can only occur when the speed of light is spatially variable". The speed of light varies in the room you're in. If it didn't, light wouldn't curve and your pencil wouldn't fall down. Light does not curve because spacetime is curved. Spacetime curvature is related to the tidal force, not the force of gravity.   

If c is the 2-way speed of light and we can't measure the one way speed, how do we know with absolute certainty that photons don't lose speed after a first bounce off of a reflective surface? 

You don't. It's because of the wave nature of matter. It's like trying to measure the length of your shadow using the shadow of your ruler. You always measure it to be the same. 

If we don't know for sure, can we say with certainty that those photons that were emitted were moving at the same speed as those bouncing off of the surface?

No. But since refractive materials don't tend to exhibit different wave speeds in different directions, you shouldn't expect it of vacuum. IMHO a more important thing to think about is your unchanged measurements of the speed of light when you start moving towards the source. People say this is due to special relativity, and you just have to accept it. But you don't. Robert Close explains it here. If you were made of sound along with your rods and clocks, you would always measure the speed of sound to be the same. 
Note that Einstein abandoned his SR postulate that the speed of light is constant. See this 1915 example in the Einstein digital papers: "the writer of these lines is of the opinion that the theory of relativity is still in need of generalization, in the sense that the principle of the constancy of the velocity of light is to be abandoned". 
