[Fiveofus]

I think you will find you need the 7 days in Kyushu. Once you get onto local trains travel is slower but JR has lovely old special tourist trains that run around these areas. We had 2 nights in Aso and wished we had another as there are wonderful full day activities out of Aso. Fukuoka needs at least 2 nights but 3 would be better to have time to explore nearby temples, eat near the river and get to the beachfront area. Shopping is good there too. I was a bit put off by the glitzy image of Beppu but it was inexpensive and fun.

If you decide to leave Kyushu and break the journey back to Tokyo Hiroshima (big 1/2 day) and Himeji (1/2 day) are worthwhile and both have a lot of cheap accommodation.