Hi!
Presumably you would go: Yufuin to Beppu by bus or train; Beppu to Yawatahama by ferry (
https://www.uwajimaunyu.co.jp/english/#routes) Yawatahama to Matsuyama via train or some other form of public transport.
From Matsuyama there are direct ferries to Hiroshima:
https://www.japan-guide.com/e/e5504.html?aFROM=2160_5500From Hiroshima to Matsue you can take the train or bus:
https://www.visit-matsue.com/access/by_highway_busIt is possible the bus is as low as 500 yen, you would need to contact the bus company to find out, since the offer was only valid through 2018, but it might still be ongoing.
You might do well with a Sun Q Pass:
http://www.sunqpass.jp/english/ when traveling in Kyushu.
It might make sense to go from Matsue to Kinosaki and then work your way from Kinosaki to Okayama and then from Okyama towards Kyoto. Unless there is a good reason (like you're overnighting in Arima onsen) it probably makes sense to just pick Kyoto or Osaka to stay in when visiting Kyoto, Osaka and Kobe. If you plan your travel correctly you can probably make use of the 5 day Pass:
https://www.westjr.co.jp/global/en/ticket/pass/kansai_wide/ Getting between Kyoto and Osaka is not terribly expensive and depending on where you are staying they may or may not be willing to hold your bag(s) which is another good reason not to change lodging so often.
It probably makes sense to move your Nagoya and Kiso Valley plans until post Matsumoto. There is the 3 Star Bus Pass you could use to go from Kanazawa to Takayama to Matsumoto. It's 5500 yen I believe and valid for 4 days?
http://www.alpico.co.jp/access/ticket/pdf/panf701[1].pdf
You would start it when you plan to leave Kanazawa. So you would do Kansai (Kyoto or Osaka) to Fukui, then onwards to Kanazawa. From Kanazawa you would do the bus route to get Shirakawa Go, Takayama and Matsumoto and you could stop in Hirayu onsen as well if you wanted. You would need to pay additional for Gokayama or any local buses within Takayama or Matsumoto. From Matsumoto then go to Nagano and then from there to see the monkeys. From Nagano or Matsumoto you can travel to the Kiso Valley and then go down to Nagoya. From Nagoya then go to Izu, then go to Kawaguchiko and then from Kawaguchiko to Hakone. You will need to price all this out since travel around Izu, Kawaguchiko and Hakone adds up VERY fast, depending on what you plan to do. Hakone and Kawaguchiko are not budget destinations.
Staying in Nagano is much cheaper than Yudanaka or Shibu onsen. Even without possible volcanic activity, the road between Shiga-kogen/Shibu-onsen/Yudanaka and Kusatsu onsen is not open in the Winter, so you would need to back track from there regardless.
You then move Kusatsu onsen to your Tokyo side of things and I guess could maybe get a 3 day Tokyo Wide Pass to cover a round trip to Karuizawa to the bus to Kusatsu and to cover travel to Nikko. From Nikko you can take non-JR trains to Aizu-Wakamatsu before going back to JR.
As it stands now you are looping around an awful lot and I think it is going to cost you more. I think you really need to spend some time working out your costs and actually checking what is open in the Winter. I think you need to make sure you can actually afford everything. Please make sure to include some money to do laundry which is going to run you like 600 or 700 yen because dryers in Japan are not always good and you will presumably need heavier clothing as you are traveling to many areas that will be cold and snowy.
Good luck!