I cut EPP foam for RC airplanes and if someone wants an easier way, there is 1 mod to your setup if you don't mind.
Instead of the Transformer you can use an Automotive battery charger and still adjust the amperage with a home/wall/light dimmer switch/knob. As for the wire, head to the local guitar/music shop or even fishing leader wire and buy some and play around with what works best on your foam/amperage setup.. I don't even remember what i settled on finally on my foam cutter since i have it dialed in so well i never bust the wire and bought something like 20 feet of it when i first started out.
You did a great job BTW... Very well done.