FRANK SHORE - Excellent idea on using RATCHET STRAPS... Should be able to fold it enough to get it in open area. You may have to let it out again however to get through the TC Door..
We purchased 3-inch foam from EBAY sales for our OFF-ROAD POPUP trailer beds and was really surprised when UPS delivered them all reduced down in size in the shrink wrap package.. I actually questioned the UPS guy if they had brought the correct item I had ordered.
I did the same thing by opening it up already inside the tent bed area and it expanded right on out for a perfect fit haha...
Roy Ken