Paint with the doors on. Hopefully you will have adjusted them beforehand. I think the potential of collateral damage after the fact is greater .
The rivet nuts that are in the body: You can use old hardware, but BA is not readily avail. Hint: I have used a piece of braided nylon twine and folded in half using a small screwdriver to push it into the thread at the fold. I have also seen a dab of latex chaulk used as well. It does no damage and comes out easily.
Let me warn you. The rocker trim is held in with a cup retainer and a "male pin" slid into the trim channel . It is basically an interference fit and the molding of the male pin it will lock into place. I removed all my body mounted trim and what happens there is paint buildup around these bare holes which change the diameter. The body part, is a softer plastic cup that will slide in (I press with a block of wood), but when the male part is pushed into it will be damaged due to the restricted opening. I went thru many male pins before I realized the issue was the added paint around the hole in the body thereby deforming the plastic pin. I also used a dab of silicone spray on a Qtip and it was the best method for me.
Go on the FS site to check out the "body clips"
Also paint shops use detail guns for door jambs and restricted areas and they have been figuring out this stuff for decades and I know you're concerned like I would be (I'm crazy too!) , the last thing he needs is a customer on his ass instructing him , he will lose interest or inflate the bill to cover aggravation.
1980 SWII LRL-41587C FInj
1976 SS LWB LRE-23114 Harkness RR