I was considering the following route, but life (and other trips) got in the way, so it might not happen this year:
From Eugene, leave town southeast via Dillard Rd. Then hwy 99 (frontage to I-5) to Dale Kuni Rd then to Cloverdale followed by south on Sears Rd. into Cottage Grove. In CC, pick up the Row River bike path and ride it to its end. At that point, take Row River Rd, which becomes Brice Creek Rd. (NF22). Take the right fork onto NF2213, which will become gravel for a few miles. At some point you will take/road becomes USFS3831 and then USFS100 and then USFS38, which becomes Steamboat Creek Rd and returns to pavement. Steamboat Creek T's at N. Umpqua Hwy, take that on up to where it becomes Cascade Lakes Hwy then Diamond Lake Bypass then Crater Lake North Hwy.
You can look at (almost) all of that on Streetview to decide whether those road surfaces suit you.