Tioga Pass is going to be a sticking point. However, snow could be hitting the higher elevations up to June, so it would be tough to avoid tourist traffic. Just learn to live with it. You could go up the east side of the Sierra if the pass is closed, or up the western foothill route earlier in the spring and cross over to the east side on the first open pass (avoid Hwy 50). Carson Pass on 88 is a good one, or the Donner Pass along I-80, or Yuba Pass on 49 as the last resort (a very nice route, though)

The route on 89 through Lassen Park could also be closed until midsummer, but there's a less scenic route around the park.