Cutting Styrofoam for Fitting on an Armature?

Your excellent info on painting Styrofoam leads me to you now. I have spent a small fortune, for an artist and sculptor, to create my collage/head. It is due on Monday by noon. My art league is very serious and I've spent weeks building up to this final step, using newsprint and good magazine pieces, to seal all over head.

Now I'm worried if I use a water-base adhesive, it will crumble. What do you think of a regular, but quality, spray mount? and how should I cut from the bottom, to enlarge the head for the 3" armature, which will give it such a great, heavy feel.

Thank your in advance so much.