Why not? Your extra axis could be on the end of the Z which is a pretty common arrangement for a machine like this.
That is nice. I might suggest though some help from fellow students doing structural engineering. You really want to look into what the minimal beam size would be for the span In question. Since saging under its own weight will be an issue you may need a more advanced design that just a single box beam. It really comes down to what you are expecting performance wise.
FYI - I already have a very nice CAM and CAD package
The idea of a moving table design is interesting but it would lead to a very large machine. For your purposes though it might be a smart move especially if you can build upon a concrete foundation. You can eliminate a huge amount of structural material with everything built close to the ground on a concrete foundation. This is a "cheap" approach but for foam ( really light work) and light duty usage it could be a smart move.