It looks to be a very punishing trip, particularly trying to go such long distances in one fell swoop at some points. Let's get back to that later.
First, I have to question if getting a Tobu Nikko All Area Pass and not use it for the round trip between Tokyo & Nikko (just around Nikko and one way back) would pay off.
The next thing is 2 days to see the Hitachi Seaside Park, Karuizawa, and Ashikaga. You didn't define which place on which day clearly, but getting from Tokyo to the Seaside Park will take over 90 minutes, and if going from there straight to Karuizawa, that is another 3-3½ hours - with earlier sunsets, you will not have much time for Karuizawa sights at all - and unless you are renting a car from there to get around, the buses are not as frequent or as fast as you'd like. I'm not sure where you are going in Karuizawa, but when I went there it was very inconvenient to get around - I only went to 2 places I really wanted, and just ran out of time to see anything else - and that was with a full day. If I had to do it again, I'd have rented a car.
If you go from Kanazawa to Hiroshima in one shot, it will take you close to 4½ hours - rather long and tiring but doable. That said, if you left around 5:30 PM you'd be arriving late into Hiroshima close to 10 PM with a good connection. Still, I'd pick that over going in the morning and all the way to Miyajima, taking 5-5½ hours and then try to do an afternoon of touring. Have you thought of maybe taking a day off of Toyama and seeing somewhere in between Miyajima and Hiroshima, like Okayama, Himeji, Takamatsu, or Kurashiki?
As mentioned, it would take over 4 hours to get from Hiroshima to Takachiho, but that assumes the bus schedule works out for you - there are only a couple of buses a day, and I am concerned that by the time you get there, you will be tired out and not have much time to do all you want. With 2 nights to try and see the Kunimigaoka Unkai, your chances are better, but of course, no guarantees.
For Miyazaki, I don't think you've fleshed it out enough - you just list the statues, which don't take that long to see. There are other nice sights though, like Udo Shrine, the Obi castle & samurai area, or Cape Toi.
Regarding Kyoto or Inuyama, you are considering apples and oranges - both are good, but the dance is not that long. Kyoto has a thousand other places you could add. Meiji Mura is absolutely worth it though as well, and it is big - you could spend half a day to a full day there. Inuyama Castle is also there, small and quaint, but one of the 12 surviving originals.
I'd never plan things the way you are suggesting, unless you are going to call it quits afterwards. But if your heart is really set on it, I wish you the best of luck.