Thanks for the replies!

As far as camping locations go, I was planning on dispersed camping on BLM lands wherever possible - As I understand it this is allowed and free?

I definitely won't be biting off more than I can chew in LA - probably just a few hours napping on the beach!

As for skipping Great Basin & Tahoe, these aren't must-do parts of the trip but I'm borrowing the car so it needs to be back in LA at the end - is there a quicker/better way to do this?