Help: California road trip planning (Late April-May)

Hello. I'd love some help planning my upcoming trip to California. We'll be landing in San Fran in late April and staying for three weeks total. We are a couple, very active, love hiking. The current starter to the plan is to drive a bit of the coast from San Fran south to Monterey, somewhere I've wanted to visit for a while, then drop into a bit of the Big Sur before cutting east across to Yosemite.

This is where I find it gets tricky. We're WAAY too late to get campgrounds in Yosemite (and we are on a bit of a budget; would prefer to camp). That's okay - happy to stay outside of the valley and drive in each day. But my next idea was drive one of the roads through the Sierra Nevada to link up with the 395 because it looks stunning. Seeing that's basically impossible in April. If that's the case, is there a workaroudn that could take us onto the 395. Because, then my next sketchy outline for the trip was going to be...

Tahoe - Gold Country (Nevada City) - Lassen - Shasta - State and National Redwoods - then back down the coast to San Fran for return.

Any day-hike suggestions would be super welcome. We're good hikers who regularly do 15km+/day on trips, though I get vertigo so hikes that are gnarly I'll need to big myself up for. Also love Western History and Gold Rush history, so that would be a plus. We're more into being in the middle of nowhere than in big towns/cities.

Thanks all!