Hi,
Yes, as you mentioned, you'd pretty much break even for Days 6-12.
For either Hakone, Tokyo Disneyland or DisneySea, it's up to your interests. Personally, if you go to Japan, then seeing Japan is best, so I'd pick Hakone. But if you were to choose one of the theme parks, Disneyland is more of the traditional Disney, and DisneySea is more of a modernized Disney with more of a Mediterranean theme. You have the time, so you could do 2 days for Tokyo, one for Hakone (get the Hakone Free Pass), and one theme park. If forced to choose, I'd do DisneySea, since there are multiple Disneylands.
For your Day 6th, I'd do a half day to see Kobe, and the late afternoon and evening to see Osaka. Kobe has its Nankinmachi chinatown, ropeways to great mountaintop views, earthquake museum, and Sorakuen Garden. At night Osaka comes alive and has some great places to see, such as Dotonbori, plus the night views from the Umeda Sky Bldg, and Abeno Harukas Bldg are wonderful.
For your Nara day trip, the sights near Nara Park are the best. The Todaiji Great Buddha in Nara is a must see. Feeding the deer is also nice, and seeing the Kofukuji Temple and Kasuga Shrine are also rewarding. A few other great places missed out even by those who go to Nara though are the Isuien and Yoshikien Gardens. They are gorgeous and not crowded at all.
Hiroshima also has a number of good places. Miyajima is the most famous, and aside from Hiroshima itself, Onomichi with its temple tour and Kosanji Temple is spectacular. Just beyond Miyajima also lies Iwakuni with its historical bridge and castle on top of the mountain.
For Fukuoka, there are many open parks, shopping, seaside historical areas, and urban neon. See this site as a good guide.
Be sure to see the Nanzoin Temple which is one of Japan's finest yet almost totally unknown to the outside world and completely FREE!
Look into a Fukuoka Tourist City Pass also.
You can also see a lot of previews on the best there is to see here.
You should have a busy but unforgettable trip!
Good luck.