I think the backroad you're thinking of is between Concrete and Sedro-Wooley. The pavement on that section reminded me of some of the allegedly paved roads in rural Kansas.

If you do take 20 across the state and need to compress a couple day's rides, I'd suggest starting early from Kettle Falls and doing Sherman and Wauconda passes in a day. It'll be a long day, of course, but the ride up Wauconda from Republic was the easiest of the four passes (in four days). Once you summit Wauconda, it's all downhill to Tonasket.