Sorry,I remember hyperdia.
Hyperdia | Timetable and Route Search in Japan.
I recommended "Takayama→Mino Oota→Tajimi→Nakatsugawa".
But you don't need to worry fare and seat fee.I correct recommendation.
Takayama→Nagoya→Nakatsugawa.
You should change train only once.It's not confusing.
How about Route2?
Hyperdia | SearchResult
Takayama→Nagoya.not so frequent.
Click "Station timetable" of Takayama on Route2 and check it.
Nagoya→Nakatsugawa. At least three trains per hour on day time.
Click "Station timetable" of Nagoya and check it too.
Nakatsugawa→Magome.Local bus. check the linked page on my last post.