Hi!
I post this all the time, but here is the TDR crowd calendar. If you want to go, check the dates here:
http://www15.plala.or.jp/gcap/disney/Having gone on an orange day this past Summer I would not recommend going on any day that is orange or darker. It's just crowded and unpleasant and really not all that fun unless you like walking around in crowds of people and waiting in lines for 1-2 hours.
In terms of seeing Mt. Fuji what do you mean by "see Mt, Fuji?" Do you mean just see it and snap a few photos, see a specific view of it? You can't climb it in March. I have been to Hakone 4x including in March and have never seen Mt. Fuji from Hakone. I know people get sick of me saying this but I have seen Mt. Fuji multiple times from Tokyo. I saw Mt. Fuji from the monorail at TDR at the end of June this year. I regularly see Mt. Fuji from Tokyo, even in the Summer. I've seen Mt. Fuji from Odaiba in March, I've seen Mt. Fuji from the Chuo line headed to Tachikawa. Now, if you want specific views or do something specific in Kawaguchiko or Hakone, then I totally get going there. But if it's just to see Mt. Fuji, you might be able to do that from Tokyo.
I will ask my friend where she stayed. We're on USA time so I've not had a chance yet. I know she went in March of 2018 specifically to see the snow monkeys.
I can't speak towards traveling to see snow because it's not something that appeals to me. I can see snow outside my window for 3-4 months a year. lol It's possible depending on temperatures you will get to walk through snow for 20+ minutes to see the snow monkeys.
Unless you time your trains well, it is going to take you a really long time to get from Shibu onsen to Takayama on day 7. You can take trains from Toyama to Takayama but they run a lot less frequently than the trains from Nagoya to Takayama. I also think if you like temples at all you should check out Zenkoji while in the Nagano area. I guess you could look into taking the train from Nagano to Matsumoto and then the bus to Takayama or Okuhida. I am not sure it would save you time though. If your goal is to get to Takayama on day 7 with time to see anything, I would definitely spend the night of Day 6 somewhere with better transit options to Takayama.
Since you want to go to Shirakawa Go, I might spent night of Day 6 in Kanazawa. You can then take the bus from there to Shirakawa Go and spend the night in Takayama. Then from Takayama you take JR to Nagoya and then onto Kyoto. (or take a bus depending on budget and such.) Since you're staying in Shibu onsen on Day 6, you can be done with the monkeys by 13 or 14:00 easily and on your way to Nagano and then onto Kanazawa. If you finish with the monkeys early you could see either Zenkoji in Nagano or Kenrokuen in Kanazawa. Heck, you could see Kenrokuen on day 7 in the morning and then take a bus to Shirakawa go and see it for a few hours before continuing onto Takayama or spend the night in Shirakawa Go and catch a morning bus to Takayama.
So I am proposing you change:
Day 5 visit Hakuba/whatever you want to do night Shibu onsen
Day 6 see snow monkeys and then possibly see Zenkoji or Kenrokuen night Kanazawa
Day 7 see Kenrokuen then travel to Shirakawa Go night either Shirakawa Go or Takayama
Day 8 explore Takayama night Takayama
Day 9 travel to Kyoto, see Kyoto (night Kyoto)
By making that change you'll overall be spending less time in transit and back tracking. If you pack light I would do more single nights, if you pack heavier, I would do 1 night Shibu onsen, 1 night Kanazawa and then 2 nights Takayama.
And I will get you that ryokan name!