I would layer it and tie it at 4-6 inch intervals - and then bind it the usual way. If really heavy, then skip the batting.
I would also consider quilting the pieced top to a piece of flannel like you mentioned.
I think it would be easier than trying to wrestle it using the birthing method. Another reason I would not use this method would be because of the bulk in the corners.
Then I would put a binding on it that would finish at about 1/2 inch (I would cut the binding fabric about three inches wide) - I would sew it on the curly side first, and top stitch it down on the front.