Regarding Ghibli, yes it is very challenging to get tickets. I tried to buy one for a weekday in August on the late afternoon of 10/Jul and no tickets available any longer... It seems to be possible to buy them 3 months ahead through JBT. I would guess it is only a limited number, so check that out.
Regarding Hakone and Kamakura, yes better to put a more quiet day in between. But overall your plan looks good, not too busy.
When you go to Tsukiji, consider visiting also Hamarikyu Garden, very nice Japanese garden on the bay.
Regarding Mount Takao, its probably still going to be nice with autumn colours. I went to Kamakura on the first weekend of December last year, and it was still nice there. Not perfect, but quite nice. You can see a picture here:
http://bicycletraveljapan.blogspot.jp/2016/12/a-weekend-out-on-miura-p...There are autumn colour reports. I would suggest to enter "g—tî•ñ ŠÖ“Œ" in your search engine when you are closer to the date, and multiple pages should come up. In Japanese, but there will be some with maps and symbols.
If in the end you decide against Takao, you might want to go to Enoshima as replacement.
Definitely no JR Railpass needed. It only pays off if you travel extensively and far (e.g. Tokyo, Kyoto, Hiroshima, Osaka, Nikko). If you are not on the "railtrack" for a long distance ride every day or two it does not pay off.
For convenience you might want to buy a Pasmo or Suica card to pay your train, subway and bus rides.