I cut mine with a box cutter or a very sharp kitchen knife and a strait edge. That heated wire sounds like a real nice tool, I'll have to look into getting one, if they aren't too expensive.
You'll need to use the high density foam. The blue or pink stuff, not the white crumbly stuff with the rough grain to it, but the fine stuff with the smooth finish. Otherwise the bees will chew it all to pieces in no time.
I've found that a thorough coating of paint, especially gloss or semi-gloss, on the inner surface of the foam, slows considerably and almost eliminates this problem. But be careful not to leave any thin spots where the bees can get started chewing.
I think I will get a sheet of the dense foam for my next batch to see how it works.