Kyushuu itinerary questions

Hi everybody,
I am visiting Kyushu in again in November.. and I have some questions..
already been to Fukuoka, Kumamoto, Kagoshima and Yakushima but I want to explore central and eastern Kyushu now and need some advice...

day 1: arrive Fukuoka in the evening
day 2: Yufuin no Mori to Yufuin: arrive around noon
day 3: to kuju mountains to hike and get back to Yufuin
day 4: Yufuin and Beppu (general sightseeing and Tsurumi mountains).
day 5: kunisaki sightseeing tour from Beppu (ending in Beppu or Oita?)
day 6: to Takachiho (very early morning) in the afternoon travel to Miyazaki and Aoshima in the afternoon if possible.
day 7: Miyazaki: Udo, Sun Messe and Obi castle town
day 8: Kagoshima: if time permits get over to Sakurajima after I arrive from Miyazaki depeding on departure time.
day 9: Fly to Yakushima
day 10 to 13: Yakushima
day 14 fly to Kagoshima and Fukuoka (or directly to Fukuoka)
day 15 fly home early in the morning

I will be using public transportation.

about day 2 to 4: is it enough time to the major sightseeing spots? so for Yufuin and Beppu about 1,5 day.

day 5-6: What is the most convenient place to stay to get to Takachiho the night before? I guess most convenient is to pass through Nobeoka, right? Or is there a possibility to go there from Beppu or Yufuin directly? (couldn't find it myself).
And is it doable to combine Takachiho and Aoshima in one day?
day 7: so Aoshima, Udo shrine, Obi and Messe Sun is 1 day from Miyazaki? Doable? What is the most convenient way to visit? In what order and should I go back to Miyazaki to get to Kagoshima the next day?


What about transportation?

Worth buying a SUNQpass? Can I buy multiple passes?

Kyushuu railpass is probably not really worth it.. because I only need to take the train from Hakata to Yufuin, from Nobeoka to Miyazaki and from Miyazaki to Kagoshima. Possibly the Limited Express Umisachi-Yamasachi in Miyazaki for day 7 (a Sunday). so maybe just buy tickets/use ic card.

All other is probably by bus..

I can still change things if it's better. But I need to start and finish in Fukuoka.
All ideas are welcome..
Thanks in advance...

SunQ Pass can be used as many time as you want.
I wouldn't do it in a day even if I drive for Aoshima and Takachiho-cho. I drove Obi, Udo Jingu, Sun Messe, and Aoshima in a day by self drive. It sounds a little difficult when you travel by public transportation. 660 class rental car works over there.

If you are using public transport. You itinerary isn't realistic. Day six for example has about 6 hours of travel time in it.

In Kuju how about here.
I visited here in my youth many times.

https://www.tripadvisor.jp/Attraction_Review-g1121560-d10304060-Review...

And how about having the outdoor bathing in the night.

https://www.tripadvisor.jp/Hotel_Review-g1121560-d1367843-Reviews-Kuju...

Thanks everybody for the replies..

It was already clear doing Takachiho and Aoshima in one day was gonna be too much in terms of travel time. But I just wanted to be sure.
Combining Udo Jingu, Aoshima, Sun Messe and Obi is too much too of course. I will probably leave out Sun Messe and use the time schedule I found and get back to Miyazaki after to get to Kagoshima the next day easier..

In March I visited Nagoya, Inuyama and Hikone castles in one day as a daytrip from Kyoto.. I spend a lot of time on the train... but in the end I was happy to do that because I was not sure when I was gonna return. So travel time is not an issue if I have enough time to visit the places I want to visit. But it is a fact I can rely more on trains rather than buses...

As a Belgian citizen I need an extra translation of my international driving permit. And I don't even have experience driving on the left hand side, so those are the reasons I will just be using public transport. I understand this is the reason it is going to take more time to get to places. It is not always about the destination, sometimes the journey (on one of the special trains maybe) is worth considering too..

Okay will probably be using the SunQpass (or more than 1).. Just need to figure out which and when..
Will look into the Kuju daytrip later.
I am just setting an itinerary to be able to book my flight to Yakushima and back to Fukuoka and to plan where to spend the nights between Fukuoka and Miyazaki.

I am looking for English bus time tables for the areas I am visiting.. Can't seem to find that..