Note that I have not yet tried this, but I was told that using an (old) electric carving knife worked well with most foam products. I have used it with the beaded foam up to 4 inches think. This is the stuff that they use as packing material for heavy electronics.
Like I said, I havent tried it with the expanded insulation foam yet, but would imagine that the results would be as good… It’s certainlt worth a try. And you probably know where all the parts are so close to Thanksgiving dinner and all…
Woodland Scenics sells a pack of long blades meant for exactly the purpose you are descibing. I believe they are about 4" long; Xacto sells them, also. They screw into any one of the Xacto handles but I like the big red one.
If you use a carpenter’s level as your straight edge, the cut will be pretty close to a clean, vertical one so long as you are careful when cutting that the upper part of the blade, near the handle, stays tight against the side of the level.
I use either the table saw or the radial-arm saw for straight cuts and the band saw for angle cuts. The dust tends to stick to everything, but it vacuums up OK. Keep the foam moving or it will melt and stick to the blade.
I’ve found that a long thin carving knife works well on one to two inch foam board, using a steel edge to guide the cut, supporting both sides of the cut, and applying pressure on the down stroke. With a knife blade there isn’t a cloud of foam sawdust produced needing cleanup.