Gorilla Glue (GG) works stellar for gluing XPS edge to edge, and would probably work for smaller sections flat to flat (haven't tried that personally). However, if left to it's own devices it expands 4x it's volume, so you would need to be prepared to add quite a bit of weight spread out very evenly (...or vacuum bag...or fill a water bed mattress on top?
), so I would be concerned about being able to get a uniform thickness without uncontrolled expansion.
I have had really good success gluing wood paneling to foam (flat to flat, of course) using 3M's Fastbond Green 30NF water based contact adhesive. Good product, goes on easy, cleans up easy, no mixing (doesn’t even say to stir or shake it), and seems to bond very well. It is sprayable, but the instructions say that rolling is preferred to get the high buildup recommended. You need to wait until it is completely dry, and with the roller technique on foam this can be much longer than the 1/2 hr listed on the can (upto an hour in high heat and humidity). It needs to be applied to both surfaces and make sure you use stickers (thin slats of wood or dowels) to separate the two pieces while getting things aligned, because once any significant areas come in contact, they are not going to come apart without destruction. (Thanks go out to Linuxmann for the lead on this product; he has had great success using the spray on method.) I do not see why this would not work equally well on foam to foam; it is specified to work on a number of different materials.