Use rack and pinion and you don't have to worry about screws sagging and whipping.
And making a 12" Z axis to allow for foam cutting will seriously compromise the ability to cut harder materials.
for a large size machine, best to use a proven linear rail system. Take a look at the mechmate, www.mechmate.com. Uses fairly inexpensive Dual V rollers and home ground steel angle. Very solid, and about as cheap as you can get.