At this length and your requirements I would go with belt drive if just cutting foam but done in a slightly different way to what your probably thinking.? Check these out. . .Bell-Everman Dual Carriage Servo Belt.wmv - YouTube
ServoBelt: amazing belt drive - YouTube

It's one belt on top of another with rollers and pinion, it's easy enough to duplicate. I've played with it a little before for long machine but found R&P was better suited to router with a heavy gantry but for light weight gantry cutting foam then it would work fine I'm sure.

If you do a search for Mike Everman beltdrive you'll find more about it.