If there are connecting rooms (i.e. they have a tile doorway or a hallway in common), and if
the tiles end up out of alignment at the edge of one room at that common area, then they
will start out of alignment in the second room. It's a nightmare.

It's actually not a nightmare! You can choose an authentic 'border/strip' tile to go between the rooms. One that I always used to use was kind-of 'cobbled'. Imagine stone pebbles sunk into a tile like an old English cobbled street. Looked really nice and also gave you chance to correct any alignment issues, especially in crappy Australian construction. I once had a supervisor who had a standard answer to any tradesman who said something like 'Oh, but it's only a few mm out' - he'd say 'Well you wouldn't mind losing those same few mm from the length of your dick then?'

It always worked, lol.