Koya-san to Nagasaki in a single day is going to be a long trip, even if you take the bullet train. It will leave very little time to look around Nagasaki, and it's a city that deserves at least 1-2 days IMO. Do you have some special reason to see Amanohashidate? Maybe you could skip that so you'll be less pressed for time on Kyushu.
Awaji Island is very close to Osaka and would be an easy day trip.
