OP checking back in here. All sorts of great recommendations, particularly from LapLap, and I'm going to clarify some points.

The first is that I'm traveling alone, so whether or not a property charges twice as much for a double as a single doesn't bother me, as I don't need the double. If anything I'd rather that single accomodations were more widely available in the U.S., as here I routinely end up paying for double accomodations when I don't need them. I travel carry-on only, so small rooms aren't a problem.

The second is that the shared bath isn't so much to do with limited financial resources as with the very relaxing, semi-social aspect of it. And that experience is even cooler if the bath itself is very nice, and I'm very specifically looking for outdoor baths. Rooftop outdoor baths (given that the locations I'm visiting aren't rural) particularly cool. So if anybody knows of any upmarket hotels that offer this experience that would also be helpful.

I have considered ryokans for at least the Kanazawa portion of the trip (so thanks for those specific mentions) but the small ones in town tend not to have outdoor baths for sharing (or outdoor baths at all) and I'd rather not have to deal with a curfew (even though I'm not likely to have a problem with one, particularly in Kanazawa). I do plan on staying at a minshuku in Shirakawago en route between Kanazawa and Osaka, so will have a nice rural experience there. The fancy upmarket ryokans don't really seem suited to the single traveler (and in fact many of them don't accomodate single travelers at all), particularly the fancy dinner in one's room. I do have a husband, but it will be a very cold day in hell when he decides that he wants to spend an evening with me at a lovely rural ryokan (or anywhere at all that requires a plane ride of more than four hours, ever).

I'm going to give a closer look to ryokan options in Kanazawa.