it looks like your handles also have batting in them, and that makes them extra hard to turn in such a small tube. If you've got enough fabric, making new ones would be easier.
Maggie_Sue's method is probably the easiest...I'd do all the pressing, then cut a strip of batting to fit in the middle two sections, refold the strip and sew. I'd then sew down the middle of the final strap to help hold the batting in place.