If you're using the hard, white styrofoam it will take A LOT of time, patience and gesso to fill in those holes. I tried it once and decided it would be better to cover it over with clay. I didn't have too many problems with paperclay cracking. I just put it on in a thin, smooth layer and filled in the cracks the next day. They were usually very small, spiderweb cracks.
Here's what the pieces looked like: Gesso
I've used the foam/paperclay method at least two or three times now. It yields a decently sturdy, easily sanded prop.
I second using a hot wire cutter. You can buy a cheap one at michael's or you can rig one up if you have some electrical skill. There's tons of tutorials for it on Instructables