I haven't studied this to any great detail so I'll admit right up front
I could be missing something here, but the idea of an infinite speed
limit between two objects in motion relative to each other does appear
to be in conflict with the physics I was taught.

Mathematically you can postulate almost anything. In the real physical
universe, unless theory (well established theory, backed up by
experiment) is wrong, what I was taught is that two objects in motion
relative to each other will observe red-shift or blue-shift depending on
direction of travel (either away from or towards). The closer the delta
speed approaches 'c' the more severe the shift. To the point where very
near 'c' essentially the objects become invisible to each other due to
the shift. So even if there were an infinite speed allowable between
objects in motion, it is a useless postulate in the physical universe.

Dave