How many nights in Fukuoka? And what would you recommend about our road trip route in Kyushu?

I'm planning our itinerary in early November and am having a hard time deciding what to do with the Kyushu leg of our trip. This is our second time visiting Japan (last one was in 2017).

See our route here.

– Is it worth staying two nights and two days in Fukuoka just to see Fukuoka?
– Or should we leave one day earlier and rent the car earlier to see more of Kyushu?
– Is Kumamoto worth stopping for a couple of hours on our trip?
– Anything else we should move around or add/remove?

Unfortunately we can't really add more days but do like to have pretty packed days and with lots to see.