Tomoe wasn't really engaged!?
Obligatory praise: This is one of the best movies I've ever seen.
Now, a theory. I don't think Tomoe was ever engaged to that guy in Aizu. Iguchi was just about to go out to fight Yogo, by Iguchi's own estimation, a much better swordsman. Now he professes his love for Tomoe. His thoughts are clearly divided. Tomoe is a smart cookie and she knows that Iguchi must not be distracted by thoughts of the future if he has a chance to win. In fact, she goes so far as to say that she won't even be waiting for him when he comes back. Now he can go into battle with a clear head. His boss has already agreed to take care of his family, so even if he dies, his affairs are settled. I think that Tomoe made up the whole engagement story just to protect Iguchi.
I know, there's no explicit proof of this in the film. But I never liked the idea that Tomoe accepted a marriage proposal, then just changed her mind because she'd rather be with Iguchi. She is a very progressive woman, so it's certainly possible that that was what Yoji intended. But it seems too easy for such a complex and subtle film.
Of course, I find my version to be much more satisfying, so that's what I imagine when I watch the film. That's one of the great things about films like this. They allow spaces for the viewer to fill in with his own imagination.
Cheers,
-Brian*