Try two products used in cabinet shops to glue hard, dissimilar materials like melamine to melamine, or bond one such surface to porous surfaces like wood, paper,etc . When I first heard of Gator Glue, I was impressed with how much it sounded like stuff I've used for cabinets, so I did some tests using Roo brand adhesive and Franklin Melamine Adhesive. Attaching scrap PE to styrene, side by side with Locktite Super Glue proved to me that either of the cab glues were superior in shear strength and allowed more working time. Bonus is that the cabinet glues thin with water (to a certain point) and clean up with water when wet, and with DNA or IPA when dry.
This is not to take away from Gator - I'm not a chemist - but the Cab glues are available from home centers or woodwork suppliers, and to my mind they're very similar and much cheaper (under $10 for a pint). I don't think Roo or Franklin would work well for thin CA applications, but for medium to thick situations, I prefer them, and happen to have a "lifetime" supply on hand.
mike