I have had pretty good luck with liquid nail for the past couple of years. I have had tombstones made from two inch foam snap in the wind but the 2x2 glued to the back to mount it to the stake was still there.
One suggestion. When putting together two pieces of foam that will be under stress add some tooth picks or even small (1/8) dowel rod between them along with the glue. This will help to spread the stress load out away from the glue point.
I also spread the glue over the whole area in a thin layer instead of a few thick bloobs. Its not the amount of glue, it the amount of surface area thats important.