JMH: Since you are travelling through Las Vegas, heading to Onion Valley/Kearsarge Pass is a ways out of the way. I would drive directly to Westgard Pass, and the CA 168 & White Mtn road junction. Since you are sleeping in your truck, there would be plenty of spots around that junction -- see the road just 1/4 mi north of the junction. There may be spots to park and sleep there, or just north on White Mtn road. There appear to be a few available side roads. Elevation there is ~7400'.
Or you could head more toward White Mountain, and pick a turnout farther along with higher elevation. Beyond Grandview, you could drive to 10k, and sleep overnight in your truck at the Schulman Grove parking lot.
I'm curious, since you are flying in, what are you doing about water needs for the several days in the dry White Mountains? Are you buying water containers, or what?
By the way, enjoy your adventure!!
