OP here.
I went with the Gorilla two part epoxy. I mixed it in a large syringe from Walmart and applied under the trim. I cleaned under the trim with rubbing alcohol before applying.
I positioned a board with a little force on top of the trim. Looks like this will work just fine.
Will remove board tomorrow.
Note: If you want to use this method, be ready to apply the epoxy ASAP, as it sets up in the syringe in about five minutes.
Thanks for the input.
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