Thanks for the responses so far.
Greg - I appreciate the link, but I need a lot of glue - a large amount of 16x24 wood frames going on the back of 24x32 styrene sheets. 2 oz doesn't sound like very much. Or is it??
Ernst - I've tried a few tubes of "construction" glue. It doesn't stick to the styrene at all.
Steve - Is all Gorilla glue the same? I bought a bottle this morning at Home Depot, and have a scrap piece of wood clamped down as I write. I'll know tomorrow if it works.
LenR - I'm not sure what SA vinyl is, but I'm pretty sure the labels are paper, with an adhesive backing. I could tear off a corner or so, but that was all. BTW - I also stuck a piece of adhesive backed velcro on the styrene. It's on for good too.