This is rigid foam insulation, right?
Perhaps you could soak the plywood you're removing in some more water to loosen the glue between the plies enough to remove at least all but the inner lamination. Some work with sanding blocks might then take sufficient care of what's left. I found a sanding block (I've long forgotten the brand) of a type that looked something like a block of salt worked nicely to clean small remnants of wood and glue off the foam insulation when I had to do some repair to my RV.
Heat might also help soften the glue, depending on what the factory used. Too much heat, of course, may well soften or melt the insulation.