If I were you I will skip Nara and choose Kobe instead. Mt rokko is a must

Any reason why you need to head back to Tokyo from Kawaguchiko instead of heading south to Mishima station and taking your shinkansen from there to Osaka?
From Osaka to Kyoto you have a few options from the most expensive shinkansen to the cheapest local train. If you search on Google Maps you can see your options including the cost.

Also, your day 7 itinerary seems quite impossible to do unless you're not planning to enjoy the scenery and location and just want to take 2 photos and cabuts. 
Instead of heading back to Osaka at 3pm, why not allocate that whole day for Kyoto? Then your itinerary will be more doable.

Yeah I also feel the Day 7 itinerary is absolutely ridiculous for the Bamboo forest - Fushimi Inari - Nishiki part. Also because the 3 places are nowhere near each other.