I'm assuming you won't be running the fridge all the time and only during trips? If you want to make it portable, why not run a portable battery pack? I did that on my recent trip, running a Dometic CFW40w, on a 768Wh portable battery, and it lasted the entire trip, 5 days.
We stayed in the furnace creek area for 2 nights, then to Panamint Springs area for next couple. I used iOverlander app to find camping spots (at least 1 mile in from road).
We haven't done Joshua tree yet, even though it's the closet NP to our home lol, but we are planning to in the next...
Yep, took the family out to Death Valley for our first time. Planned for months, and the unexpected rain/snow fall kept us from visiting a few places (Racetrack and Titus canyon). Overall, great experience and highly recommend!