The follow up -
The decorative trim ended up being easy to pry off. It was held on by short staples. It inserts into the decorative plinth block at the top, and just slides down and out, once you've pried the rest of it loose. No staples pulled through, so the surface looks perfect.
Beneath that are two layers of 3/8 ply, held on to the edge of the slide by 3 3" #10 wood screws. I was unable to remove these backers without at least taking the plinth block off, and perhaps even the top horizontal trim, which was turning the project into something bigger than I wanted to deal with. So I didn't get behind to fill the stripped screw holes. I tried first just tightening the original screws but judging by how freely they spun, their holes had already been partially stripped at the factory, and my accident just made it worse. I upgraded to #12 screws, with glue on the threads. It was then an easy matter to use my brad nailer to remount the surface trim (after clipping off the legs of the original staples, of course).
There is a 1" edge trim, and the strip closest to the entertainment center had also been pulled loose a bit by the collision with the door. Most of it was still firmly held by staples. No way to get the nailer in a position (or to nail by hand), so I just squirted in some wood glue, and then clamped it down overnight.
Not a super sturdy repair, but it should last as long as everything else in normal use, and if I ever have the same accident again, it will fail in same way!
The door is proving to be more of a challenge to piece back together well - I've relegated it to be a winter project since the 5th goes into storage today. I'll ask the dealer for a quote for a replacement, just in case, but I know I won't like the answer!
2012 Ford F-150 Eco, Max/Max
Jayco 26.5 RLS, Reese Sidewinder