What's the best way to cut 1-1/2" or 2" styrofoam sheets? *I don't
have a "hot wire" cutting tool.

You can buy a knife blade that fits in a jigsaw (the smaller size of
reciprocating saw, that is). I've found that it goes through solid
foam like butter - it probably moves fast enough to create heat
without melting very much. Unlike cutting with a razor, I don't get
the little tear-offs either. The only way I've seen the blade at big
box stores is as part of a "variety pack" of blades.

Henry