Need glue that will stick

[Willie]

You might try BARGE Infinity cement. Says it will work on vinys, PVC, Polyurthane and other material.
Don't know if it will work for your project. Might contact the maker and see what they say.

[Drew Wiley]

Barge Cement is a classic slow setting flexible shoe glue high in hot solvents - not a good thing to breathe! It's also quite flammable.

[BKP]

Lots of good advice above. What worked for me, was to cut a "door skin" to fit into the window space perfectly but 1/2" longer on the horizontal dimension so it holds itself in tight by the springiness but also notch out a finger access hole in one corner for easy removal. I also have a rubberized fabric made for that purpose years ago. The door skin blocks most of the light, I use the Styrofoam panels, sandwiched between coreplast with a 1x2 furring strip perimeter for other purposes but would work there too. bkp

[Ulophot]

Thanks again, all. I have opted to purchase some more (Frost King) air-conditioner surround foam, which comes as a 40+" length of 2-inch-square foam. I have cut it into four 1"-square lengths and will replace the current, thin foam around the edge of the insulation with this, after trimming the insulation board appropriately.This, as mentioned above, has worked fine with the other window. If still needed, I'll spend for the double-sided tape Drew recommended.