I am going to be working under the assumption you know the opening and closing season for Kamikochi and the Alpine Route or you can look on line to check that info for yourself.
Honestly, I would subtract one day from Kawaguchiko. While a lot of the places in the alps look quite close on a map, speed limits are low and travel outside of the actual Hokuriku shinkansen itself can be slow going and hourly or less often.
Personally, I would probably take the 8:30 bus from Kawaguchiko to Hirayu onsen:http://bus-en.fujikyu.co.jp/highway/detail/id/38/
and get off there and transfer to a bus to Kamikochi. Otherwise you are looking at a 3-4 train trip to Matsumoto before then transferring to Kamikochi there which is going to take you another 2+ hours by bus and train. I suspect taking the bus to Hirayu is probably the fastest method. Overnight in Kamikochi
For day 2, you take the bus back to Matsumoto and transfer there for Nagano. If you leave early enough I would check out Matsumoto Castle. From Nagano, you then need to transfer to the private line to Shibu onsen. I would then overnight there. Depending on when you left Kamikochi you would have time to see Matsumoto and/or Zenkoji before heading to Shibu onsen. I would see the monkeys on the morning of day
For Day 3, You can either take the bus to Ogiawa from Nagano to start the Kurobe Alpine Route or go to Toyama to start.
I personally think this sounds exhausting and every day you will be spending hours sitting on various transport, but hey, maybe you enjoy that.
If you wanted to add in an extra day, I would overnight in Toyama or Ogizwa, so that you can start the Kurobe Alpine Route super early and you would then wouldn't be in a huge rush on day 2 and day 3 trying to make connections, so it would be more like:
Day 1 take the bus to Hirayu and then transfer to Kamikochi (overnight there)
Day 2 spend morning in Kamikochi and then take bus to Matsumoto, train to Nagano and overnight in Nagano. If you go to Kamikochi in July or August I think there are direct buses back to Nagano. We always seem to just miss their starting date.
Day 3 Go in the morning to see the monkeys and then overnight in Toyama or Ogizawa.
Day 4 Do the Alpine Route and overnight in Kanazawa before heading to Kyoto the next day.
A lot of people here would say this is too fast. But your original 3 days really cuts things tight. The Kurobe Alpine Route seems to be quite popular and it can get backed up.