I had an open tube of 3M 08509 Bedding & Glazing Compound (the butyl rubber stuff for our windshields and back glasses) so I just ran a bead around the areas I wanted the plastic to stick to, and pressed it into place

The Weatherstrip Adhesive will stick very effectively, but it may be hard to ever remove the plastic again without destroying it. Same for double-sided foam tape, or contact cements...