Hi Niko, Interesting concept. I use a foam cutting in my business and I can safely tell you that this would work. One thing I would change is to make your "bow" similar to the old style woodcutting bowsaws, with a turnbuckle to increase tension on the wire. Wire tension is very important in foamcutting. The thicker the cut the more important it is. For all practical purposes, Id go with leadscrew and nut on both axis. On a smallish machine its very easy to make a backlash free leadnut that pretty much eliminates any play. Plus it makes it easier to calculate steps per inch and such. Some software will only interpolate circles if steps per inch is identical on both axis.
Im not sure what motors you have or are planning to use, but Im pretty confident that all but the smallest stepper motors would have plenty of power to both move and hold your upright axis. They are very powerful for their size at slower RPMs, and you are right slow and cool is best for what you will be doing. I suppose drawer slides would work, but they to tend to get stiff or bind from time to time. Plus it would be very hard to align them to run freely in the opposed manner you have them set up since you would need to align both up and down as well as the exact distance between them, looks like a shimming and adjusting nightmare. For me, stuff like that never just "works". Feel free to email me if you have any questions.
Ed Rees
erase42@aol.com