In my quest for how to prep surfaces of crazy shit I'm testing I came across the following. http://www.epoxyworks.com/26/pdf/Gluing_plastic_Gflex.pdf
Polycarbonate should bond pretty good. I believe it's made with biphenol which is in most epoxy hardners and so should react/breakdown to form a chemical bond of reasonable strength
1800psi should overpower the strength of the foam.
As to a delam I've tried tto pouring or using hand tools to inject epoxy and haven't found a way to get it to spread out the way you need it too.
Now that I think about it.
Weighing down the delam, tight but not too tight then drilling an intake port and an outlet port and infusing a low viscosity infusion resin between the two followed by bagging the CRAP out of the finished product would be a fun thing to try.
No guarntees it would work, but if it's crap you're probably not too much further behind as you still had to cut out the delam section anyway. http://www.boardlady.com/bottombubble.htm
Epoxy and urethane cores should have no compatibility issues.