A belated thank you to everyone who replied — didn't want to post here until I had time to post a thoughtful followup.

There's a ton to go through here and I'm sure I've just begun to scratch the surface, but I already see a few options that might work.

I apologize for not being clearer about location — the reality is that we don't have a strong preference for where it falls in the trip as long as it's after we leave Osaka and before we return to Tokyo. So nearly everything mentioned here could work. I have been a little hesitant to book something in the mountains of Hokkaido as it seems like we'll be there at an awkward time of year — the Westin that AlwaysAisle mentioned appears to be closed the whole month of April, as was another property I looked at that I can't find now. That makes me suspect that other stuff might be closed as well. (We did go to Miyajima on our last trip, which I forgot to mention.)

But really anything on the way to Kyushu or in Kyushu would be great, as would something we could do in between Sapporo and Tokyo. Something like Karuizawa might even work well, as we could get there fairly easily by train from Haneda after flying out of Sapporo. (I'd tried to make something like that work for Kawaguchiko but if you don't get an early morning express train, it's a very long ride.)

I particularly appreciate the suggestions for Aomori and elsewhere in Tohoku — those hadn't even come up in my earlier searching — and all the details on options in Kyushu (which does seem like the most obvious place to fit something in). We had been thinking of trying to fit in a stop in Unzen anyway, as there's a restaurant there (Beard) that we'd enjoyed in its previous incarnation in Tokyo. Nagasaki Joe — am I correct in assuming we'll likely want a rental car to get there?

Regardless, I have a lot of homework to do — thank you again to everyone!