Wonderful land!
It resembles the Southwest, broadly speaking.
The movie has an internal division between Acte 1 and 2. The long drive in Acte 1 looked like Subaru land. None of those 4x4 could compete in the wide open spaces in Acte 2, either, lol. However, there are a few moderate sections in Acte 2 where having mild mods would be an excellent idea. One is at the outset. The rocky river crossing at around the 38 min mark looks like the single biggest challenge.
I think I could do all I saw with my minimum-mods setup and brand new oversize tires (29" probably better than my once 28.4" ones; stock is 27.6, which is what mine are now). A front skid plate that does not eat 0.5" of clearance (1.25 cm) would help. Someone with a car like mine might need to build up a bit that river crossing, though, did not see it well enough to tell. Obviously, water levels can make a big difference at different points.
Do they do road maintenance every spring? Or on as-needed basis? Do they get heavy rains over the summer? I assume that May/early June might be the driest, as is here, alongside mid-Sep to late Oct. Of course, May gets hot for the uninitiated!
Have a great time, looks like a fantastic adventure!