Like Karen, I have little or no exposure to the Japanese culture on matters such as this. However, I have seen plenty of bi-cultural couples who basically have two weddings - one for each culture, making whatever accommodations to each side they are comfortable with.

Then again, have you asked your parents if they are willing to haul themselves over to Japan to go through what sounds like it will be quite an ordeal for them? If your future m-i-l refuses to leave the city, aren't your own parents entitled to make their own decision about whether or not to take part in this ritual?

Why not set the date for your wedding in the US, and then offer to go over to Japan for the traditional ceremony as part of your honeymoon? (Possibly allowing your parents to opt out if they prefer.) You can offer her parents the option of coming over to your US wedding or sitting tight and waiting for the Japanese one, but at least it's then their decision and they are presented with a fait accompli when you arrive in Japan. And if the m-i-l pitches a big hissy fit or something, you can postpone the Japanese ceremony - indefinitely, if necessary.
Cheers,
Bev