For Christmas I made my ex-MIL a memory quilt and by the time I added all the pictures I wanted it ended up being HUGE. I had the same issue you're having.......where am I going to be able to lay this out to make my sandwich?
I ended up moving my couch temporarily into the kitchen and using my living room foor. It worked out great, I got the space I needed and it turned out, everyone LOVED sitting on the couch in the kitchen, chatting with whoever was cooking. Even after I was done with the quilt sandwich, I left it in there for a few days and my kids protested when I finally moved it back. They're still trying to convince me we "need" a couch for the kitchen now.