3 Week Itinerary Help

I am planning a 3 week trip to Japan in October, and am wondering what peoples thoughts are on this itinerary. We just want a good mix of different places and things to do. We are likely planning on getting a JR pass for 3 weeks.

Day 1 to Day 4: Kyoto . We will basically have 3 days in Kyoto since we arrive relatively late in the afternoon on Day 1. One of the days will be for a day trip to Nara
Day 5: Travel to Koya and stay there overnight
Day 6: Leave early, travel to Hiroshima and Miyajima. Stay overnight.
Day 7: Explore Miyajima. Possibly climb or cable car up Mount Misen. Travel to Tokyo, stop at Himeji on the way.
Day 8 to Day 13: Stay in Tokyo. Allow 2 or 3 days for day trips
Day 14: Travel to Matsumoto, spend afternoon and night there.
Day 15: Alpine Trail to Kanzawa.
Day 16: Spend day / night in Kanzawa
Day 17: Travel to Osaka *could maybe add another day in Kanzawa or Matsumoto instead of one of the Osaka days, or add in a trip to the rail museum in Nagoya
Day 18-Day 19: Osaka
Day 20: Leave Osaka early for airport.

I think your plan is possible.
I guess if you can use HANEDA airport,you can cut more moving time.

For Day 7, you have to set off from Miyajima about noon to see Himeji and reach Tokyo before 10pm. (Thats about the time i sleep)

You will spend 2hours JR MIYAJIMA_GUCHI to JR HIMEJI station by SHINKANSEN.
(JR SANYOUHONSEN MIYAJIMAGUCHI ~JR HIROSHIMAby rocal train.　JR HIROSHIMA ~ JR HIMEJI by SHINKANSEN)
and You will spend 3hours Jr HIMEJI to Jr TOKYO station by SINKANSEN.

Day 6 and 7. I don't think you are allowing yourself enough time for both Hiroshima and Miyajima. You will miss a lot since you are adding 3-5 hours of travel on each day.