Tokyo to Osaka via Hayakawa, Takayama

Hi All,

We are a group of 4 travelling for the first time in Japan for 16 nights. Outside of the major cities, we really want to experience the traditional Japanese villages like Hayakawa, Takayama and Shirakawa but we are really struggling to assess options around the best way to travel.

I know trains are super efficient but given the remoteness of some of these villages we are thinking that driving out from Tokyo to Hayakawa and then drop the car somewhere near Shirakawa might be an option? Can we please get some suggestions if we should hire a car from Tokyo or take a bus to say Mt Fuji and hire from there and drop off at Gifu-Hashima Station to take bullet train to kyoto?

Any suggestions/help would be really appreciated. Thanks

Indicative Itinerary:
City Duration(nights)
Tokyo 3
Hayakawa 2
Takayama 1
Shirakawa 1
Kyoto 2
Osaka 2
Sakai, Nara 1
(sapporo and around) " 3
Tokyo 1