I'm not real sure how you could accomplish the 2 layers at a time unless it is by hand, and even then, I would not encourage it because I have no idea how your quilt would hold up to it in the long run; maybe someone else here can advise on that.
I think Patrice has given you the best possible solution to the problem. Your quilt will lie flat, it will require the least amount of work on your part, & it will be the least frustrating in the end. Best of all, your quilt will still be beautiful.
Good luck! :D