First of all, Thou Shalt Not use several frames of reference at once unless you know what you're doing or you risk being badly confused.

I think that this is important; I have come to suspect that I am somewhat confused.

I think you are trying to apply to Minkowski spacetime an intuition that only applies to Galilean spacetime

This is more than likely correct. I would also note that I have been applying, over very long (intergalactic) distances, the assumption that there is no expansion, which is clearly wrong. I suspect that I should probably look more into General Relativity before continuing along this train of thought.