...yes it's abit ambitious. Not impossible of course, but harder to enjoy much when it's hectic. You'll actually spend 1 day travelling for a night in Takayama and then a night in Shirakawa Go. Also it depends on what mode of transport you took.
What happened in my previous trip:
Day 1-3 in Nagoya
Day 4 - Travel to Shirakawa-Go. We left in the morning and arrived in Takayama around 4pm. Stayed a night there.
Day 5 - Check out Hotel @ 11am and make our way to Shirakawa-Go. Arrive appx 3pm. Stayed a night.
Day 6 - Check out from the gassho-zukuri @ 10am and make our way back. Arrive Takayama ard 2-3pm. Continue journey back to Nagoya - arrive in Nagoya @ 9pm.
Day 7-8 - Nagoya
Even then, it was really tiring. In Nagoya, most of the days we visit surrounding places. Only on the last free day that we made a side trip.
However, we utilize the Seishun 18 Kippu. Our travelling cost was low but also meant a longer journey as the pass only allows us to ride the Futsu (local) and Kyukou (Express) train. Even on Express, it took us a long journey. You may be able to save on time if you spend on the tickets.
Thanks! ya, after studied a bit - i find it is actually tiring and transportation is costly too. I will just focus on the below
Dropping Matsumoto too due to distance and jr tokyo wide pass doesn't cover until matsumoto.