Just a line of thought:
For instance, I'm building another cartesian gantry based cnc hybrid machine, that basically works a bit like the MPCNC or maybe more like SPONZ's Rascal CNC, and is made from steel only. The MPCNC and the Rascal are probably a bit easier to assemble though. The advantage of mine is the possibility to fairly easily add an extra x and z axis at one end for hotwiring. Reason for choosing this type of system is that I really
do want a hybrid system, that I can use for many things, like plate foam cutting with needle or laser, 2D/3D routing, hotwire foam cutting, coarse 3d printing, maybe plasma cutting and whatever else I might think of along the way. This
is however a somewhat complicated solution, that takes up a lot of space, both in use and storage. Doesn't make my solution or MPCNC or the Rascal bad in any way, they are just like that to be able to do more different things.
BUT! If what you want to do really
only is to cut flat foam sheets, something along the lines of a Phlatprinter might be a better option? It's a transportable box, about a yard by 1 ft by 1½ ft in size, that works a bit like a large sheet plotter, with the foam moving back and forth through a pair of rollers, and the router or needle head cutting from the underside moving from side to side in the box. It would take up far less space when not in use, and possibly also be a bit cheaper to build.
You can find the opensource instructions on openbuilds.com; Main structure is a box made from a set of plates cut from MDF, a number of rollers and a cutting head inside the box moving along a rail of sorts with the cutting end pertruding through a slot in the surface the foam slides forth and back on.
Given the limited need for movement in the Z direction, that could probably be handled by a simple servo moving the cutter maybe up to half an inch up or down. Then it just needs 2-3 stepper motors for the x and Y axis. If you build it smaller to just take DTF, 2 might do.
an example of one in use. I'd use Linuxcnc or machinekit on an old pc in stead of Mach3, as they are free/opensource and just as good, or alternatively run it from an arduino board with a GRBL variant or similar, but that is generally more about personal preference.
Another space saving option could be an adaptation of a maslow 2D or 2.5D CNC router system (
https://www.maslowcnc.com/). Ditch the heavy router for a much smaller one or a needle cutter, place the 2 servo motors at each end of a 5-6ft 2by4, hang it firmly and accurately(possibly with finely adjustable height at one end?) from the ceiling, and have a removable ~ 2 by 3 ft work surface centered at or below table height a bit in front of the 2by4 and tilted back to line up with the pull lines. Oh, and replace the heavy chains with GT2 toothed belts, they are both lighter and cheaper. After end of use remove or fold away the cnc work surface, and your workbench, etc. is cleared.