Late May/June and the snow "might" be melted enough.
As CarFree said Mckenzie pass "might" be plowed and melted.
The Aufdeheide from Hway 126 to Oakridge "might" be melted ( it's not plowed ).
And Hwy 58 is a major truck freight route. Going east you WILL be riding uphill, on the shoulder, single file, next to slow moving trucks. ( Taking the lane would be suicidal ). Going west ( clockwise ) would be better, not good, but better.
FS Road 21 turns to gravel, and the connection between it and 58 via Summit lake is a rough/non-maintained dirt/pumice road, with snow drifts as late as July.