Do you have some fabric that would go with what you have for backing and make a border on the backing that would wrap around the front for a binding?
I'm thinking if you are lacking 2 inches ( that would be one inch on each side + the 1/4 inch seam...making it 1-1/4 in. to get to the edge on each side), then if you had something to make a 3 inch strip to go all the way around........that would give you 1/4 inch to make up for the seam on the backing...1 inch to get to the edge on the back ( on each side )....that would give you 1-1/2 inches to play with for the hem on the front.
If you having a strip of anything to practice on, just sew it by hand for a short distance and wrap it to the fornt to see if it will work. Wish I could be there to help you, because I may not be clear with my instructions.
It could add some interest to the quilt. Please let me know.
If you don't have a strip that's long enough by itself, you could piece a border if you have any scraps left from the quilt.