My initial thoughts:
The trip is doable, but Hokkaido is bigger than people realise and you will doing a lot of driving - not NOT use Google map time estimates, they are totally unreliable and journeys invariably take far longer than Google maps tell you.
Skip Nemuro area - its totally uninteresting. Rather, head south from Akan and do the Kushiro marshes. From there, its a fairly easy drive along r.38/r.392 to the motorway for your drive to Chitose.
Given what you seem to like, the time of year and your schedule, I'd recommend skipping Sapporo. Others may disagree, but to me, its a rather dull, big city, and you could see plenty of other amazing sights instead.
If you are doing Biei/Furano, make sure to take in the Senbotoge pass coming into Kamifurano - the views are great.
As the previous poster said, Soungyo Gorge is a MUST, but chances are you'll be going through it anyway on your way to Akan. I'd recommend taking the cablecar up, then hiking the last bit up to the summit.
If you are approaching Akan from the north via r.39, I'd recommend taking r.243 to Kussharo lake. The views from the top of the pass on the approach are fantastic. When you hit r.52, turn left and follow the lake round and then onto lake Mashu - again great views.
Btw, just before the turn-off to r.52, there's a small peninsula jutting into lake Kussharo that has a couple of free mixed bathing onsens where you can enjoy some nice views while you wallow...
On the road south to Kushiro, off r.1040, there are fantastic 360 degree views be be had from the viewing tower at Tawadaira camping ground.
For pix and reports on my trip round Hokkaido last year, visit the pages round here:
https://myjapantravels.wordpress.com/2015/10/08/usuzan-volcano-memoria...