You are going very fast. I don't know what you are planning at each location, but the usual amount of time in Kyoto is 3-4 days, and that also goes for Tokyo.
My general advice is to get to a city the night before. Many places, such as shrines and parks will close around 5 PM, and you can use the evening to get to the next location. In the morning, check out of your hotel and have them hold your luggage while you visit the city, and return in the early evening to get to your next location.
I am assuming that you have looked at the YakuMonkey Paperback or online guide for Yakushima Island. I am giving you the YakuMonkey link to the bus timetables.
http://www.yakumonkey.com/2012/05/new-yakushima-bus-timetables-2012.ht...I would recommend the Kotsu Sightseeing bus, which will also take you to your hotel. Do the "A" tour the first day, and the "B" tour, which will end at Ando Port about 20-30 minutes before the Jetfoil departs for Kagoshima. The Jetfoil will depart at 13:30 and arrive at Kagoshima Port at 15:30. You can take the bus from the port to Kagoshima-Chou Station.
I don't know what you are planning to see in Kumamoto, but it is less than a hour away by Shinkansen. After leaving Yakushima Island, I went of the east coast of Kyushu. I know that Mount Aso can be closed due to gaseous eruptions. You may want an alternate plan, such as going to Beppu if it is closed.
Your plan to visit Miyajima is fairly good in terms of tides and seeing the shrine and the floating gate.
March 4th
9:04 High Tide (+3.20 meters)
15:06 Low Tide (+0.81 Meters)
Miyajima is on the Seto Inland Sea, which flows out to the Pacific Ocean, so it is always a little above sea level, even at low tide. You will see a "floating" shrine and Tori Gate in the Morning, and a "beached" shrine and Tori Gate in the afternoon.
You might want to go to Hakone instead of Fuji. Hakone is south of mount Fuji, and is accessable from Odawara, which is a Shinkansen Bullet Train Station between Kyoto and Tokyo. If you like transportation, you might like the Hakone Round Course.
http://www.japan-guide.com/e/e5210.htmlThe trip does seem fast to me.