I would glue and put a couple of small screws in place just to help hold it. Make sure you pilot drill the screws so you don't split any of the wood.
Glue the joint, clamp it, pilot drill it, drive a couple of #4 wood screws and call it done.
I like the razor scraper idea. So far I have been using a hammer drill to quickly pull the non-glued parts of the particle board. Then I get a small putty knife and drive under other loose parts (easier than doing the same with a pry bar). I then “rake” the glued down parts with the hammer drill (wide chisel tip), which lowers the height of the remaining ...
Use the two part epoxy and drill a pilot hole for the self-tapper to get started in. Take care to only drill through the material, as there may be something beneath that doesn't like being drilled at the same time.
I would drill out the plastic and glue in a plastic rod of a suitable diameter then re-drill the hole as necessary.
This does of course depend on the thickness of the material that is being worked with.
Another option is to glue a fresh piece of plastic behind to give more support to the screw.