I want to do a loop through the Alps Region by rental car - but need some suggestions as to how to avoid one-way rental car fees

We are in Kyoto and the beginning of our trip, and in Tokyo at the end.
In between we have 5 days/4 nights that we'd like to spend exploring the Alps region by rental car.

My original plan was to take the train from Kyoto to Takayama, rent the car there, do a day trip to Shirakawago/Gakayama, drive down to Magome do do a day on the Nakasendo, and then drive to Matsumoto, return the car there and take the train to Tokyo.

I'm having a really hard time with the one way rental though.

Looking at the map, I'm now trying to figure out how I can do all this in a loop so I can pick up and return the car to the same spot whilst not backtracking or crisscrossing the country by train if that makes sense.

Can someone give me some tips or suggestions please?

Train from Kyoto to Matsumoto, do the loop from there?
Or train from Kyoto to Takayama and go from there?
From anywhere else I haven't even thought of?

Little background info:
Family of 4, kids 10 and 12 (so 4 lots of train tickets for each journey)
from Australia, so driving on the left is normal to us
have international license
have experience in driving overseas in different countries
travel time early Oct

Thank you! I can't seem to work out how this makes the most sense.