You have 9 days listed, and the JR Pass is good for either 7, 14, or 21 days. Suggesting which JR Pass will depend on what you are doing in Hokkaido. That said, there are several things that will not be covered with the JR Pass.
Actually, there are 11 days, if you consider the extra in Tokyo, and going the following day to Hokkaido. It is a very long distance be rail. Are you flying?
There is a JR line from Nagano to Mastumoto, so that is no problem.
There is a Bus, or, the Private rail to get to the Monkey Park:
http://www.japan-guide.com/e/e6027.htmlShiakawa-go is also by private transportation:
http://www.japan-guide.com/e/e5953.htmlThe Alpine route.... Well... You may be seeing a pattern here:
http://www.japan-guide.com/e/e7551.htmlAnd the Kurobe Gorge:
http://www.japan-guide.com/e/e7575.html#/section_getThereSo... lots of the things that you are doing will cost for private transportation, and a JR Pass will not help. But, it will help for getting BETWEEN cities.
It depends on what you are doing in Hikkaido, and how much use the JR Pass is up there.
If you are willing to move things around a bit, I can suggest the Hokuriku Arch pass, and the Tokyo Wide Pass. This can be accomplished by moving Kariuzawa to the end of your journey.
Start by activating the Hokuriku Arch Pass on arrival:
http://www.japan-guide.com/e/e2361_arch.html1) Tokyo to Nagano for 2 nights.
2) Nagano to Toyama for 2 nights.
3) Toyama to Kanazawa (rail) and then a bus to Shirakawa-go for 2 nights.
4) on the final day of the pass, go back to Kanazawa, and take the Shinkansen to Kariuzawa for 2 nights.
On the day you leave Kariuzawa, activate the Tokyo Wide Pass:
http://www.japan-guide.com/e/e2361_06.htmlThis is a three day pass.
Day 1: Kariuzawa to Tokyo
Day 2: transpotation around the Tokyo Area.
Day 3: Transportation from Tokyo to the Airport.
This may work for you. Good Luck with your planning.