I think you could use a "quilt as you go" method to add borders made up of top, batting and backing. There are several books and methods to do this on Amazon. They basically sew a border and batting to the quilt to either front or back, then add the other border layer by making a flat fold or whip stitched seam.
Or if you have access to the edge of the quilt batting, use a fusable wide cloth tape to attach additional batting. Then sew borders on top and bottom.
It might be a little awkward or labor intensive, but it can be done. Good luck.