Wow. Good guess on LC and I feel the same about Cleghorn. Whole Mojave Road is an idea. If it wasn't for the fact that one end is pretty far, you can drive it in a weekend. That is as long as you don't explore. I normally spend the night at the AVI Casino then head out. I don't really want to do that until this whole thing is over. That place is great for people watching.
I was up there last winter. We went in at Baker and bypassed Soda Lake. You NEVER want to drive on that unless it's completely dry. The mud is so caustic, it will eat through thinner paint and rust everything. It is fun to slip/drive on though. You get stuck and your probably spending the season there until it dries.
Whats your time frame? If you wanted to do the road with exploring, its a few hours to the far end. Come in there, drive for a couple of hours and camp somewhere. During normal times, the river entrance has a bunch of ATV's and Side by Sides camped there. Can be noisy. That's why I would recommend going in a bit.
One of the first canyons had a wash out a few years back. The bypass had a mining area next to it I would like to explore.
About half way there is a "secret" group camp that's nice. Its about half a mile off the side. At the 2/3 mark, if you haven't explored the New York Mountains, there's some great higher elevation sites to camp. These are nice if the trip is hot.
Depending on time frame, 2.5 day's +. 3 with small exploring. 2 long days just running through. I personally like taking my time but I'm good either way.