I sent 2 quilts to a long-armer who trimmed the batting and backing right up to the edge of the border. There would have been no fill from the batting for the binding. So, I widened the seam allowance from 1/4 inch to 1/2 inch and then I could turn the front, back and batting into the binding to finish it. The only tricky part is the corners, and where to stop before making the turn. I fudged it and the corners seemed to turn out ok. I did several test seams to make sure I could turn the binding and cover the seam line, and it worked out. It is worth a try.