In case, if you decide to stop by Beppu. Here is the very infromative website explaining Onsen in Beppu. But it is all in Japanese!! (Couldn't find English counterpart)..
http://onsendo.beppu-navi.jp/
And, this is how Beppu Onsen Passport look like. This is 2013-2014 version, the latest one.
http://onsendo.beppu-navi.jp/topic/1493.html
If you decide to visit Kumamoto, there is a Kurokawa Onsen in Kumamoto (so, you don't have to boil your brain about squeezing Beppu). Kurokawa Onsen is very popular amongst Japanese. My parents loved it very much.
Kurokawa Onsen
http://www.kurokawaonsen.or.jp/english/
As for your itinenary, that 7-day Kyushu trip?! I will be exhausted by the time I reach Hakata with that much activity packaged in.
I agree with you that maybe stick to selected few places in Kyushu for, say 5 days? (Fukuoka, Nagasaki, Kumamoto, left top-half of Kyushu)