If you're really set on gluing it down, I would recommend getting an adhesive that is more suited for the materials. Wood glue is really only very good on glue.
I think even standard CA Superglue would be better than wood glue for this application. But something like a gorilla glue, or some sort of epoxy would likely be an even better option.
Or if you know that 3m adhesive works well for you, just pick up another bottle of it. I just don't see the plexi adhering very well with wood glue