There is lots of painters primers for foam surprised they didn't know about them to make it simple. Jesso solution comes to mind in addition to Sobo as opposed to Elmer's glue which does not have much
effect on foam - for starters. What do other tech people use?
One thing especially with expanded poly but it also works with extruded poly as in this case is that spray paint does not work well with foam panels to paint them. The
vehicle/aresol in the can melts it down. However done properly with say your
base coat color or better yet a primer coat, that melting down can add a easy texture to the foam once cut into
block size, plus the paint and melting once dry will form the
foundation for other colors to
build upon it - no glue needed.
As an experiment, take a sample panel of white - expanded poly styrene, and a similar panel of Blue Dow Board or as it's called extruded poly styrene as it's the same basic suff, only it was extruded out of a machine under pressure and that didn't allow the little white dots to completely form. Anyway, from a range of about three feet, try a light stripe of spray paint once across each sheet. Just one. Than move a
bit closer and try another one. Go for a third from this range, but do either a slower swipe or two of them to compare and see how the effects of distance and amount of material on the surface reacts with the foam. I'ts kind of interesting and an easy way to make texture besides with a blow
torch or other chemicals.
Also there is some contact cements that can be rolled on specifically for foam that once dried would form an adiquate
base for paint if not attaching one panel to another.
Router was a good choice but you have to have a variable speed one or if too fast it's going to melt it's way
thru the foam and trash an expensive blade. For the foam moulding at the Osmond Theater in Brampton Missouri, I was using a 2"
cove bit at about 200 RPMS at one
point. I was amazed but could not let the
router linger in any one spot or it would cause melting. Back in college an instructor once tought us about using a table saw diagonally to do similar things. Very cool but you had to set it up just right and use the right materials. Foolish me, having seen that but not thought, I tried the table saw with foam padding as one might see under a chair. That foam got hooked into the blade and sucked into the saw before I knew what happened.
I have made a lot of stupid mistakes over the years or more properly learned from them that's why I'm out there in preventing people doing the same. Such tips above hopefully lead you on to other things you can do or try, much less spur on more debate and techniques.