Not sure I properly understand the structure you’re describing.
Are you producing a box section for the surface the Shapeoko will stand on?
I built a torsion box out of fairly cheap grade plywood (similar cost to MDF). It’s glued and screwed at the joints. Everything but the legs is plywood to avoid warping caused by regular wood expanding and contracting, MDF would do the same.
This one is way deeper than it needed to be, even just a couple of inches deep ends up being surprisingly rigid, the key thing is a top and a bottom plate with some bracing to hold them at a fixed distance from each other.
I suspect that just bolting the machine to a surface will likely form a more rigid structure, but if the surface isn’t fully flat this might cause the machine to change shape as the surface does.
Got any pics of what you’re planning to build?
As for the doors and sealing, I never got round to putting the top on mine so I can’t really advise on that, there are loads of threads where people have made excellent enclosures though, as well as a couple of Winston Moy videos on YouTube;