KT: I have a solution for you. Cut the carpet on three sides of the hatch (not the hinged side), Cut a little square so you can mount the hatch pull ring. Bind the three cut sides (or not depending on whether you think the carpet threads will pull out along the cut edge). Now you can just lift the ring and the carpeted hatch will come up without the need to roll up the whole darn thing which is what I had to do, too, before coming up with this solution. The carpet can be held to the hatch either with screws (every 8-12 inches with a finishing washer on the top for appearance) or double face carpet tape. I vote for easily removable screws. If I had a shot of the floor I would insert it here.

Did the same thing at the entrance to the v-berth to get easy access to the shower sump pump. And for access to the space under the galley table.

These little tricks have saved me mucho aggravation over a dozen years the "new" carpet has been in place. Good luck with your project