I understand about Wikitravel. It is too bad that official tourism website of Yakushima is in Japanese only. If you really want to entertain the idea of visiting Yakushima, then JAC (Japan Air Commuter) has 5 daily flights from Kagoshima by Bombardier Q400 (74 seats prop plane), 30 minutes flight. This will give option of visiting Kagoshima area (possibly Ibusuki and Miyazaki area added) and Yakushima in one week.

JAC also has flight from Fukuoka once a day also on Bombardier Q400.

JAC 3671 Fukuoka 12:50 p.m. – Yakushima 1:50 p.m.
JAC 3672 Yakushima 1:35 p.m. – Fukuoka 2:35 p.m.

With this flight I think it is reasonable to do Fukuoka and Yakushima in one week. I think it is not that much of stretch to add Nagasaki to this.

JAC is part of JAL so you can get Visit Japan fare which is 10,800 yen per flight segment but have to fly in and out of Japan on OneWorld airlines. Welcome to Japan fare is 28,080 for two flight segments which is slightly more than Visit Japan fare but you do not have to fly in and out of Japan of OneWorld carrier for Welcome to Japan fare.

Yes, cannot see entire Kyushu in one week, but I think Yakushima and one other Kyushu location is possible for one week travel.