I've been spending sometime repairing some of the interior panels of my 1926 Tudor. Someone years ago either installed a cheap replacement kit or made their own. Anyway, I been having trouble with keeping the panels tight against the frame of the body or doors. The panels are held in place with some small rose bud clips that are expanded with what looks like a dry wall nail. These clips, at least in my car will not stay in the holes of the frame and doors. They will pop out and then the nails will mar the finish of the moldings.
Since some of the panel were warped and needed to be replaced, I decided to try using some modern plastic clips. I purchased some Balkamp 655-1125 from NAPA
These clips are for 1/4" hole, which is the size of the holes in the frame and doors. I punched 3/8" hole in the new panels. This allows a little movement of the panel to better align it to the frame or door. To hold the clip onto the panel I used a small patch of duct tape (the handymans secret weapon).
So far the panels are being held securely. I have some poly wool between the panel and the fabric which hides the clip head. I think it looks good. Time will tell if it stands up.
I believe those ring-shank nails were original as were the clips. I think the vendors sell a plastic replacement clip now. Your fix is a good one and should work great. No points off for that one.