Kunisaki as daytrip

Hello!

After reading so many recommendations, I am considering to spend some time in Kunisaki but I am not sure if my idea is too rushed or on the contrary is feasible...

The start point would be Beppu. With a rented car. Our idea is visit the Rokugo Manzan Temples. Some of them at least.

In this case, what about starting in Beppu, drive to Futagoji, and then Fukiji and Makiodo. Anything else recommended?

Later come back to Beppu to just overnight.

Is this reasonable or too much packed? Excessive driving time or not that much? Representative of Kunisaki peninsula?

Next day would be a train transfer to Fukuoka or Nagasaki... Optionally we could finish our day in other place connected with those cities by train like Usa but as we won't have time to visit maybe is unnecessary to pack/unpack things... Just a thought...

Thanks a lot!