I just saw on the weather report that the southern Sierra Nevada mountains (Yosemite area) are currently at 180% of normal snow pack, with more rain/snow in the forecast. IMO, the best E-W roads in that area are the passes, Hwy 120, 108, and 89 (south to north). Right now, I'd guess your chance of making it over all of them in early May are iffy. That snow is DEEP. You can get good info on line from Caltrans and the CHP--just google "Cali highway conditions."
As for your ride down the coast, both 36 and 299 are very fun rides, but they don't get you south. They get you inland from 101 and you really don't want to come to California to ride I-5. Take 101 out of Eureka, see the Avenue of the Giants, and make the turn not too far south of there at Leggett where you'll leave 101 and get on Hwy 1 toward Fort Bragg. The first 50 miles or so is super twisty, elevations changes, gorgeous scenery through old-growth redwoods and very little traffic. Lets you off on the coast. You can follow 1 as far as you want. You may never want to get off. Believe me, you'll be right on the edge of the continent for many miles. Amazing views, twists and curves you won't believe, and again, very light traffic. It's just too twisty and scary for most any car driver, but for an FJR? It's heaven. You might just want to stay on Hwy. 1 all the way to Mexico.