Well, did you invoke any 'random' behaviors, e.g. Game and Watch's hammer? It seems that sync is maintained until something random occurs. I haven't done exhaustive research on why dual-core causes unpredictable behavior on our two computers, but the only noticeable side-effect is the fact that the RNG does not sync, and apparently it can also fall out of sync during load screens (but doesn't always.)
I'm testing on the same computer, so I'd like to think that the tests are pretty "clean."
edit: Sorry, I posted before you edited. Yeah, being able to resync is a good idea, and I hate to duplicate code, but I'm highly interested in attempting to implement this feature myself. If it's desyncing only between rounds, and nixing randoms is enough to make dual core work for this game, that would be possibly solvable. At the same time, though, the important thing is that we can play right now, with any character, only issue being the CPU tax of single core. This is what our thread is all about.