Andrew -- I live in Kumamoto now (starting my fourth year here), but work at a university which gives me almost 5 months (paid) vacation a year. Owning my own school would definitely NOT allow me that amount of time off! The only down side is having to stick to school holidays.
Ron, I don't know if you've looked at this site yet, but it, and the book that the guy sells is an excellent resource to Yakushima. You can fly there from Osaka (Itami), Fukuoka, or Kagoshima. The prices on his site seem a bit low compared to what I checked. Of course you could take the ferry from Kagoshima as well if you have a little more time.
FWIW, you can only book flights within Japan within 60 days of your planned dates. That is also the best time to buy tickets, because they'll be at their cheapest then.