My dh did it for me. He is a perfectionist, so he laid out the foam on a piece of cardboard, marked his cutting line, then used a metal ruler to keep his knife straight as he cut down. (The foam was laid out flat, not on edge.)
I think there are different types of foam insulation; our pieces were styrofoam. His cuts done as above were much neater on the edge than the piece he had to carve out with a knife for the sewing machine, which shredded the styrofoam more.
It turned out great, but I have to re-do the vinyl covering. Not being a quilter, he cut a slit in it all the way to the needle and a quilt would catch on those edges.