Yes, going via Matsumoto is a little more expensive unless you have a railpass, or take very slow trains. But it's very doable even in one day. For example, you can leave Kyoto at 7:45, arrive in Matsumoto at 11:03, leave Matsumoto at 18:03 and arrive in Tokyo at 20:52. This leaves a nice big chunk of time to see Matsumoto, and see nice scenery along the way.

The two-day version would certainly work well. You may know this from other threads and sources, but you can hike between Tsumago and Magome in the Kiso Valley and the tourist office will transport your luggage from one village to another for 500Y, so it is there to meet you at the other end. Tsumago would be great to stay in overnight. When all the daytrippers leave, it really seems like it is an old town and very quiet. There are inns there that are very accepting of western touristrs (it seems--I didn't actually do it). (Magome is more of a recreation--not so authentic-seeming.) Then you could do Matsumoto the next day.

I did a Kiso Valley/Takayama/Shirakawa-go/Kanazawa/Toyama/Takayama (again)/Nagoya trip a few years ago using all trains and buses (there is no train to Shirakawa-go). It works out well, but you have to plan it carefully. I enjoyed using the public transportation--it takes a little time but was interesting.