The constructions you show work OK for a small 2'x2' machine, but will result in a very poor 4x4 machine. If you want to build from MDF, everything needs to be torsion boxes, not just the table. The gantry sides should be 3" thick torsion boxes. The gantry beam should also be a torsion box, at least 4"thick x 8" tall.

Your Z axis as shown will not be nearly strong enough. I suspect it will be very loose, or will break very quickly. Using the skate bearing on pipe method requires that the bearings be forced very tight to the pipes. You have no way to do that with the Z axis.

Most of the members here build only in aluminum or steel, and wouldn't even consider MDF. My personal belief is that it's very possible to build a good machine from wood. However, it takes a lot of knwledge, skill, and techniques that add considerable time over metal builds.

I believe that the design you've shown will not work very well at all. My suggestion is to build a small 24" x 36" machine, and you'll see where the shortcomings are. You'll gain valuable experience that you'll really need in order to build a much larger machine.

And don't even think about using corian. It's not flat, it's brittle, it doesn't hold screws well, it's not very rigid. It's just not a good choice for building a CNC machine.