Hi Hunty!
I would say it´s a tricky thing to try discussing a practical design for a Hotwire on such a theoretical level. Eventhough i for myself really like every thinking in that overall direction, and am prepared to talk about the coulomb laws, the three kirchhoff laws and the movement of free electrons within metalbonding etc., i don´t believe the basic laws of physics will save you from making big mistakes if you fiddle with your fuseboxes at home for example. In that sense i´d say doc has given very good advice on the practical side, and was probably just simplyfiing the physical background in order for everybody to get a basic picture. Naturally the flaws get in there, but it´s no use discussing those. doc is right in pointing out, that the maximum amperes limit your system rather than the voltage. This is because we are talking about a metalwire here and not about something unconducting like for example air, which requires a minimum of 40000 volts per meter to get conductive.
Just put a big screwdriver between the poles of your car battery and watch it glow white in a second throwing sparks, if you think 12 volts are lame.
maybe the simplest way to go for you, is to take your bow and change one end, so you can push the main cable alongside your wire, to alter the length of it´s hot part. But you have to make sure, that the connection has enough contact, because otherwise it will be your hotspot (as doc has already explained). you could curl it around,if it´s a solid copperwire. This way you can adjust the temperature, try it on the foam, and see if the remaining lenght is enough. If it is not you could use your car battery for short term maximum power, for it has way more amperes than the charger.
Anyway as a kid my modeltraintransformer did hotwire the foam for a modelkatamaran very nicely, after i burnt lots of wire and my little fingers anyway. Later in the project i was horrified, when the paint dissolved my hard work.
regards - d.