motrohome travel big pine, ca to scotty's junction, nv

I would take the route out of Lone Pine to Stove Pipe Wells. Enjoy the great scenery. We camped at Stove Pipe Wells for years in the winter before it was a Natl park. We always got hookups because everyone else wanted the free camping. Suppose now you would need reservations for those hookup sites.

One more thought, sounds like you are there, or going to be there anyway so why not take the car for 30 miles drive to high point and see before considering motorhome drive?
I bet the scenery is going to be beautiful as all those passes are.

MAP

This is probably the only pass in Sierra I did not take so can't give you personal experience, but those passes are pretty difficult and even I drove 40' via Yosemite, it is not recommended.
Looking at the map it is not going to be easy and you will need lot of brakes.