Asahidake to Sounkyo trail and return

Hi! I'm planning a two-week trip to Hokkaido next July and would like to walk the trail between Asahidake Onsen and Sounkyo Onsen. We will probably rent a car for the few days before going to Daisetsuzan and will need it for the remaining days.

My idea was to leave Sapporo in the morning for Funaro, visit the countryside during the afternoon and to sleep at Asahidake. The next morning, hike between Asahidake and Sounkyo and sleep there (get the luggage forwarded to Sounkyo). Then, I would have carried on with the trip (to Wakkanai & Cape Soya).

The big issue is if I leave the car at Asahidake, I have to go back there which means a 4 hours bus ride or a very costly taxi bill... and a terrible waste of time.

Any idea? Should I simply travel through Furano & Biei by train, take the bus to Asahidake... then the bus again between Sounkyo and Asahikawa where I can rent a car? It seems to be to be a disaster of logistic with no contingencies for unexpected events.

In the worst case scenario, would it be better to stick with one area (Asahidake or Sounkyo) and do it by car? I always wanted to travel across a national park in Japan and it would be great if it could be possible to do it over the Daisetsuzan, but if it means stressing over bus schedules, it's completely counter productive. If you have any suggestions, let me know. I'm aware many people here did the hike between both places.

You can buy hokkaido budget bus pass 3 day
=11000 yen, 5 day=17000 yen valid sapporo, hakodate, wakkanai,asahidake,furano, biei

And don't forget to pick up the English Hiking Map ASAHI-DAKE Hiking map 1:25,000,The heart of the Daisetsuzan National Park before you go. The best map available with lots of background information:
https://www.amazon.co.jp/dp/4906740278/?language=en_US
Covers your walk. Enjoy!

Thanks Khan! I reworked the schedule to visit both sites at different moments. I'll be able to see both places without hiking from Asahidake to Sounkyo and dealing with countless hours of bus.

Thanks for the map Hausi! I've heard about them, good to know where to get them.