Which JR Pass to use?

Hi there!

That's one of the best itineraries I've seen recently. Visiting Kyushu is amazing and so is Okinawa.

I would recommend a 14 day JR Pass for your 2nd and 3rd week. Just traveling from Tokyo - Kagoshima pay for the bigger part of the JR Pass (Tokyo - Osaka ¥ 13,750
Osaka - Kagoshima ¥ 21,300). With all the extra travel you'd be making very good use of the Pass.

If you return to Kagoshima after Okinawa and want to take the train back to Tokyo, then I would would recommend the 21 day JR Pass (gives that you can make the return in this amount of time).

Hope this helps and have a great trip!
Daniel