I am now considering to avoid to move from Tokyo to Kyoto directly. You do have an interest in Hakone and Nagoya. Then, why not put these sites between Tokyo and Kansai.
Checking express buses,...
2500 06:30-09:20 Nagoya-Umeda
2550 07:10-09:44 Nagoya-Kyoto
3000 12:00-15:47 Nagoya-Namba
3400 07:30-10:31 Nagoya-Sannomiya
3800 09:40-13:55 Kyoto-Kanazawa
4000 07:20-12:16 Umeda-Kanazawa
4200 08:55-13:02 Kyoto-Takayama
4700 07:50-13:02 Umeda-Takayama
4700 07:35-13:02 Namba-Takayama
and selecting the two most economical ones, the following could be made.
KIX
-(920 yen, 0:51/Nankai)-Osaka/Namba
-(560 yen, 0:54/Kintetsu)-Nara
-(620 yen, 0:42/Kintetsu)-Kyoto
-(3800 yen, 4:15/bus)-Kanazawa
-(1850 yen, 1:15/bus)-Shirakawago
-(2470 yen, 1:07/bus)-Takayama
-(1660 yen, 2:21/JR)-Toyama
-(10850 yen, 7h)-Shinano Ohmachi
-(670 yen, 0:54/JR)-Matsumoto
-(2150 yen, 2:36/bus)-Mt Fuji/Kawaguchiko
-(1750 yen, 1:45/bus)-Tokyo/Shinjuku
-(1184 yen, 1:45/Odakyu)-Hakone Yumoto
-(310 yen, 0:14/Hakone Tozan)-Odawara
-(5080 yen, 4:36/JR)-Nagoya
-(2500 yen, 2:15/bus)-Osaka/Umeda
-(320 yen, 0:40/Hankyu)-Kobe/Sannomiya
-(1130 yen, 2:08/Hanshin+Nankai)-KIX
The last one uses Kanku Access Ticket,
http://rail.hanshin.co.jp/uploads/otoku_pdf/416932cfebf0e681c4e3f255c2...while this one might attract your interest.
http://www.kobe-access.jp/en/index.phphttp://www.kobe-access.jp/en/fare.html