You don't say if you're quilting on a longarm or a DSM. I have a friend who quilts about 30 quilts a month on the two machines she owns, mostly for charity. She doesn't have time or energy to iron backings. When she gets one that is badly wrinkled, she'll load it in the evening, spritz it with water, and let it hang to release the wrinkles.
If you don't have a frame, then I guess I'd go the damp dryer route.
