You are traveling very slowly, which is not a bad thing. I also do not think a 21 day JR Pass will be cost effective. There is also a section (Shirakawa-Go) where transportation is essentially by bus.
I am going to suggest using a Willer Bus pass for three legs of your journey. This nice thing about this pass is that it is good for three or five transportation days within a three month period.
https://www.japan-guide.com/e/e2369.htmlI am going to suggest moving Nagoya, and walking the Kiso Valley to much later. I understand putting Hitachi Seaside Park and Yoshino later, so that it will fall into cherry blossom time.
How about the following:
Get a 5-day JR East Nagano Niigata Area Pass, and use it to go to Nikko, Nagano, and a side trip to Matsumoto from Nagoya. The pass will end while you are still in Nagano, so do whatever side trips, like Matsumoto, that would be covered by the pass.
https://www.japan-guide.com/e/e2361_nagano_niigata.htmlTo get to Kanazawa, just pay for a train or bus to get there. This is the first use of the Willer Bus Pass.
To get from Kanazawa to Shirakawa-Go requires bus transportation. I think going through Takayama makes sense to get to your next destination, which should probably be Kyoto. All this can be done by Nohi bus line.
https://www.nouhibus.co.jp/english/In Kyoto, a daily bus pass is probably the best way to get around, so once again, you do not need a train pass.
At this point, a Train Pass might be useful. Since you do not actually say where you are going on Shikoku Island other than saying you are going to walk or bike the Shimanami Kaido. Take a bus or ferry to Shikoku Island. There is a Willer Bus that goes to Matsuyama, so the bus pass could be used here. The ferries leave from Kobe and Wakayama. Check out the Japan Guide Transportation section for more information. The JR train pass may be useful, so I will put a link in.
https://www.japan-guide.com/e/e2357_shikoku.htmlAfter the Shimanami Kaido, you will start your journey back towards Tokyo. You are going to Osaka next, so this is the second use of the Willer Bus Pass.
I am going to suggest a 2-day or 5-day Kintetsu Rail pass to get to Yushino, possibly Nara, and the to get to Nagoya. If you get the two day, use the Willer Bus pass to get to Nagoya.
https://www.japan-guide.com/e/e2357_006.htmlYou will either do a train/bus, or just use busses to walk the Kiso Valley. At this point, you need to get back to Tokyo. So this is the final use of the Willer Bus Pass.
I hope this gives you a framework on how to work on your transportation issues.
Good Luck, in planning you trip.