Ok, I don't think I did a good job of communicating this, so here's a better way to phrase the experiment.
There is a spaceship traveling horizontally in the x-direction at near the speed of light (let's say .866c). On its bow is a clock composed of two mirrors, stacked vertically in the y direction, with a light pulse bouncing back and forth between them, each bounce counting as one "tick". On its stern is an identical clock. Engineers on the ship use a laser to calibrate the light clocks so that they are in sync (as described by Einstein).
The ship is observed from the reference frame of a donut shaped space station on which another light clock exists. The ship passes through the plane encircled by the space station. The following measurements are taken based on when the ship breaches and exits the plane:
A: The station records the number of ticks in its own clock between the breach and exit of the ship.
B: The station records the number ticks it perceives in both of the clocks on the ship between the breach and exit of the ship.
C: The ship records the number of ticks in its own clocks between the breach and exit of the plane.
D: The ship records the number of ticks it perceives in the clock on the station between the breach and exit of the plane.
How will these measurements compare? Is there something flawed in my logic or setup? It seems that both frames of reference will think that the other persons clock is slow. Which will be right based on the values of A and C?
This post seems like it answers a very similar question: The Four-Clock Special Relativity Conundrum
I can't quite make the interpolation from that scenario to mine though. My feeling is that it has something to do with the fact that the station will not perceive the clocks on the ship as in sync.