Very interesting post, PeeVee. I think you’ve pin pointed a problem I have with my hot wire cutter!
My hot wire cutter used NiCr wire (from eBay) which has a higher resistance than copper and gets hotter with less current flow. P = I*I*R. NiCr is also the wire used in toasters and heating elements.
Anyhow, my hot wire cutter glows red hot when running, but I used 22 gauge wire and not the thicker 12 gauge stuff you’re talking about. That might explain a problem in my design.
When I’m cutting at a slow pace, the wire glows red hot and cuts like a hot knife through butter. However when I try to pick up speed, the heat from the wire gets sucked out too fast by the foam, the wire cools, and you can’t force the cut any faster or else you’ll break the wire. With your thicker wire, it might be less prone to lose heat to the foam and hence let you feed stock at a much faster rate.
What happens with your cutter if you don’t feed the foam through at a constant speed? Do you get a variation in the kerf of the cut?