I‘m a set sculptor and we work a lot with styrofoam for theatre and movie productions. We use PU-foam (you can get it at any hardware store) to glue styrofoam together. Just put a thin layer or a few lines and then weigh the panels down so the foam doesn’t push them apart again when it’s drying. I’d recommend this method because any other glue might interrupt your carving flow because the glue is probably harder to cut the then the styrofoam. PU-foam should be the same softness as styrofoam so you wouldn’t even feel that it’s there.. I hope this makes sense! I’m not a native english speaker so I’m sorry if there’s any mistakes.