LapLap

There's an overnight bus. Costs about 8,500yen.
http://transportation.fujikyu.co.jp/...nghere/04.html
Takes 9 hours to Kyoto, 10 hours to Osaka - don't gasp yet, wait for the alternative...

I suspect (but am not sure, I don't read or write Japanese) that this is what the seat would be like on this route http://www.fujikyu.co.jp/syonan/kintaro.html

With your itinerary I would DEFINITELY not recommend the JR Pass.
You shouldn't avoid travelling by train though. The JR pass makes sense if you plan to whip up and down the country within the 7 days. It effectively costs 4,040yen per day so makes sense if your travel costs are this or greater than this sum.

It costs 2,560yen and about 150 minutes to get to Kawaguchiko from Shinjuku, Tokyo by train OR 4,070yen and 140 minutes from Shinagawa.

From Kawaguchiko it's 15,500yen for the 6 and a half hour trip to Osaka - See! Makes that 9 or 10 hour overnight bus option on a reclining seat seem much more sensible!

Travelling AROUND Kawaguchiko by train would be cheap and easy. Roughly 1,000yen or so for every hour spent travelling (it's the high speed express and bullet trains that push up the price per hour as they cover so much more ground, Japanese trains really aren't that expensive when you take out the intercity sprinters from the equation)

An alternative way to explore the country and perhaps see Mt Fuji might be a return trip from Tokyo to Hakone for 5,000yen (includes cable car and gondola and boat rides) http://www.odakyu.jp/english/freepass/hakone_01.html and then get a Shinkansen (or overnight bus) to Osaka
13,800 yen and 146 minutes (or 173 minutes if you get the JR pass)
Even this option would give you 4 days to somehow spend 10,000 on rail fares, which would be difficult given your plans for the Kansai area - after all, it's only 1,200yen for the 88 minute train trip from Osaka to Wakayama
And roughly 3,000 yen for a return trip to Koya San on the non JR (I.e. JR pass not valid) Nankai railway.