Oh man, what I wouldn't do to have your studio. First I would rearrange the furniture so I could set up a folding cutting table (or 2). There's no way I could be up and down on the carpet. The cutting mat could be hidden under the carpet when not in use to keep it flat. Yep-I've done this in a pinch. The sliding shelves for your fabric is the way to go.
With all these suggestions, I know you'll use your creativeness and put it all together to your liking. Have fun!