I can't imagine hand sewing the binding on the front of the quilt. It seems to be a really tough job, but it must have been done by those long-ago quilters before sewing machines. It can be done, but be sure you have very good, strong thread and knot every couple of stitches (back stitch or ...) to make sure it's secure.
Another suggestion: Call your local quilt shop and ask if they know some one who can machine sew it for you. Just a thought or two.