I do the same.
I do a basting stitch where I think the future seam allowance is going to be. Then I lay the quilt on the floor with my biggest mat underneath and cut the excess away. I am able to double check the straightness against the parquet flooring by lining up my long ruler with the squares. I move around the whole quilt this way - makes the corners square. If I cut off some of my basting I pin that portion to hold the sandwich together. Then I sew my binding on.
Every time I do a large quilt this way I swear I'll never to it again. Never crawl on the floor again. Never, never, never. I don't listen to myself. When I finally manage to get up I head to the medicine cabinet for pain relief and die the rest of the day. :)