"The question is this: given the high speed and curved path of the ISS, what should we expect to see happen with an object that has active gyros in all 3 dimensions if we were to observe for 1 minute or more?" - Robo
The ISS is falling around the Earth. The gyros would also be falling therefore they should maintain their position inside the ISS... However, with 3 gyros active inside an imaginary box the box should orbit its axis once for every complete circuit of the Earth that the ISS completes because the gyros would keep their axle perpendicular to their spin... In other words, on one side of the Earth the top of the box would be pointing to the ceiling of the ISS then on the other side the top of the box would be facing the floor...
I believe that is correct based on my knowledge of how these things work... I may be wrong!