Hey Chris, thanks so much for taking the time to write all this up! I had heard of time-dilation and that space and time are linked to form spacetime. I didn't know, however, that this necessarily means that time is non-orthogonal to space, in other words, that it's impossible to travel through time without also traveling through space.

Oh, and for the record, I don't mind at all discussions like this. I love debugging my brain and discovering flaws in my thinking :-)