Well, after pondering option - the tension bar wouldn’t stay in place - I thought of a small bean bag to just hold the trim in place.
Searching around I found ‘Corn Hole’ bags and I could get them in black. At 20 Bux for 8 it seemed worth a try. And it works. the bag weighs a little over a pound.
While I was messing with the trim I felt way up on the back side, and I could feel the particle board (bare!).
But with the overlap of foam lined cloth a direct gluing seemed out. Then it occurred to me that I had just the stuff - Museum Putty.
It’s used to keep things from sliding off shelves or keeping pictures straight on a wall.
So I slipped a small wad back there and pressed the trim into place and it’s staying.
I don’t know how well it will hold in the heat of summer, but it looks good now.