It matters not what "speed" they are travelling, the two observers are stationary in relation to the light source. To an outside observer in the rear the light is shining in the infra-red, to an outside observer placed in front of this conveyence the light is shining in ultra-violet. Both outside observers "see" the light at the same time (assuming they are equi-distant from the source when the light pulses), as do both stationary observers.
Show me proof (from CalTech, MIT, Stanford or Cornell, not some ninnyhammer that has some kinda axe to grind) that C is different "east to west" than it is "west to east". This would be an observable, repeatable and provable, violation of Special Relativity, which of course has not happened. E still equals mass times the speed of light squared, and in a vacuum, light always travels at a speed of 299,792,458 meters per second, no matter how its speed is measured.
On the gripping hand, at 1/2 C, the visible light coming from the direction of travel of your unlikely conveyance has now shortened to hard X-rays and has killed the two observers.
The Sagnac effect is explained here:
http://www.mathpages.com/rr/s2-07/2-07.htm Pay particular attention to:
"Special relativity for a Sagnac device are correct and entail no logical inconsistency, the dedicated opponents of special relativity sometimes resort to claims that there is nevertheless an inconsistency in the relativistic interpretation of what's really happening locally around the device in certain extreme circumstances. The fundamental fallacy underlying such claims is the idea that the beams of light are travelling the same, or at least congruent, inertial paths through space and time as they proceed from the source to the detector. If this were true, their inertial speeds would indeed need to differ in order for their arrival times at the detector to differ. However, the two pulses do not traverse congruent paths from emission to detector (assuming the device is absolutely rotating). The co-rotating beam is travelling slightly farther than the counter-rotating beam in the inertial sense, because the detector is moving away from the former and toward the latter while they are in transit. Naturally the ratio of optical path lengths is the same with respect to any fixed system of inertial coordinates."
This shows that the times of flight of east-west vs west-east are unequal.
Now look at my flatcar experiment. The path lengths of the light are unequal, as it is moving. Let's say it's moving with an astronomical radius in a circular path to make it "non-inertial", but for the time of flight it's virtually inertial. According to the Sagnac Effect, the light arrives at two different times because the length of each light path is different. Since the observers see unequal arrival times, but they sense only inertial movement because of the large radius, they can only conclude the speed of light is different in the same "inertial" reference frame.
So how do you resolve this?
FYI:
http://www.physics.umd.edu/rgroups/quantum.html "The East-West vs. West-East light propagation time experiments are being reactivated with the use of circular scan streak tubes as timing devices. It is hoped that resolution of ~ 10 ps can be achieved. The direct comparison of the one-way propagation times on the rotating Earth has never been done at this precision and in this way. Our knowledge is not secure as to whether the speed of light should be ± c or v ± c, where v is the tangential speed of the Earth's surface. "
US Naval Observatory:
http://tycho.usno.navy.mil/ptti/index9.html Differential Comparison of the One-Way Speed of Light in
the East-West and West-East Directions on the Rotating
Earth; C. O. Alley, R. A. Nelson, Y. H. Shil, J. T.
Broomfield, J. A. Fogelman, M. A. Perry, J. D. Raynor,
C. A. Steggerda, B. C. Wang, M. J. Chandler, and L. J.
Rueger