Hi!
I will do my best to answer some of your questions, but first...
Takaragawa onsen and Shirahone onsen are really not very close to one another. Even in a rental car you're looking at 4 hours one way. So I think you are either headed to Takaragawa onsen on the 7th OR headed to Shirahone. You're not easily going to both.
Please also be aware that from Miyajima to Koya-san is over 5 hours of travel if you are using a rail pass so you can't use Nozomi Shinkansen. With a Nozomi it drops travel times down to a little under 4.5 hours, it's still going to be a long travel day.
Shirahone has some lovely looking ryokan as does just outside Matsumoto itself. I know @LikeBike stayed overnight at Hirayu no Mori, I only day tripped there. It had splendid onsen. The Okuhida region also has some great onsen. I would be cautious about driving from Matsumoto to Takayama. The drop off fee is going to be around 10,000 yen or more. I looked into it once a year or so ago. The further the prefecture for drop off is from the prefecture the car was rented from the higher the fees. Someone on this forum recommended the Kamikochi Onsen Hotel in Kamikochi. It poured while I was in Kamikochi so it was not something I considered visiting as a day guest.
Have you thought about Kaga onsen near Kanazawa or Wakura onsen on the Noto Peninsula as your additional onsen overnight? You could hit one of those on the way to Kyoto.
You could also look into an Izu Peninsula or Atami on your way back to Tokyo from the West. I don't always want to stay at a ryokan, but I try to get in as many onsen or sento experiences as I can when in Japan.
For the Moto GP, it looks like it is near Utsunomiya and Mito. I've been to the Mito for its garden but I've never stayed over night. There seems to be a glamping site nearby
https://www.twinring.jp/f-glamping/stay/You can but Motegi Moto GP in Google maps and just look for accommodations nearby. Depending on when your flight home is, just make sure to give yourself time to reach it. There are lot of ryokan at Nasushiobara which is not so far away from Motegi.
I'm a huge fan of Kanazawa so would always recommend an overnight.
You can rent a car, but please remember if you're not on an expressway (which will have tolls) the speeds tend to be low. And again there are huge drop-off fees and some places, like Kamikochi, don't allow cars. You'd have to price out your options. There are certainly pluses to rental cars, just always be aware of the cost. I'm pretty sure there was not a lot in the way of gas stations between Matsumoto and Takayama. I've been on nearly the entire route via bus. I would not want one in a big city as parking fees can be quite high and spaces can be hard to come by.
Good luck!
