craftgrrl | I Need Some Sewing Advice!

My former husband decided to use my sewing skills to hem his canvas signs for an outdoor festival. He had already marked where he was painting and told me to cut the ends off so that my hem would be equal distance from the markings, which I did.

Little did I know (he didn't tell me this btw), that there was an empty spot on one end because he was planning on drawing in and painting something extra that wasn't marked, so I ended up cutting off too much.

Rather then start all over again (he'd already started painting it), I'd like to just attach that piece to the end and re-hem. Could someone give me an idea on what sort of finish I can use on the raw edges of that fabric (on the backside) that will protect it from fraying? I definitely don't want anything that will cause any extra bulk or that would require extra stitch lines along that seam. We're wanting this as camouflaged and flat as possible. Thanks!