Kyoto-?-Tokyo in 1 day?

I have a JR 7 day-pass, and I would like to take a one-day side-trip on my way from Kyoto to Tokyo. My travel date is July 20, and I think it's a holiday.

questions:
Should I stop by Nagoya or Mishima (then go to Kawaguchigo)? I did a quick look-up, I think I can arrive Kawaguchigo by noon if I take 1st train out of Kyoto. I will take Fujikyo line to Otsuki and take JR to Shinjuku.

Am I crazy to crank so much in one day if choose to go to Lake Kawaguchi before return to Tokyo? I think I can check in a Ryokan, have lunch and take a hot spring bath with Mt. Fuji in the backdrop.

Any Onset recommendations in Kawaguchigo?

Will the train be busy the evening of July 20?

Please help.

Yes, it is feasible to make a short visit in Kawaguchiko along the way via Mishima and Otsuki. Transportation back from Kawaguchiko to Shinjuku can be expected to be rather busy because it is the last day of a long weekend.