Back in the '80s I was touring around that area. I broke an axle coming down hwy 44 into Redding and it took several hours to get it replaced. By the time we headed out hwy 299 towards the coast, it was after noon on a Friday. The traffic was horrendous and the road was not exactly bike-friendly. After one of us was nearly pinned to a wall by a bouncing, empty flatbed, we decided this just wasn't going to work. We got off the bikes, crossed over the road, and walked on the shoulder while guiding our bikes on the road surface. For some reason, the motorists gave us a lot more room when we weren't on the bikes. We left hwy 299 at hwy 3 and continued on to the coast via hwy 36. It was a sweet ride on hwy3 and hwy36, although parts of hwy36 were only one lane wide.
As we approached the end of hwy 36, an old-timer told us he wouldn't even drive on hwy 36 monday through friday. This was back during the Maxxim debacle; they had every logging truck on the west coast hauling the last of the redwoods out. We just happened to miss that by being there on a weekend. That shouldn't be an issue now.
If I were you, I would look at heading south before venturing west. Maybe take A16 to hwy 36. Good luck.