Have you tried Gorilla Glue? Do a test sample first. Otherwise, how
about "Liquid Nails" in one of its incarnations? I've used that when
nailing trim/molding was difficult or awkward. One-way trip, however,
in both cases.
You might look at "Titebond Melamine Glue". It specifically mentions
bonding to vinyl, though I haven't used it myself.
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