Yeah, just take a seam ripper and remove all the Velcro, re-position the Velcro to desired position and sew using polyester thread (e.g., gutermanns thread). Stitch around the perimeter of the rectangle and then do a crossing X. The stitching will look like a box with an X in it when done. You can take it to any drycleaner type tailor and they can do it quick. I could even do it for you for free ( I live in Brookline) just give me at least a couple of hours. Good luck!
EDIT Rereading your post I think it's easier to add another slab of Velcro then to remove the current one and reposition. It takes more work to remove/reposition/resew. Also I've never encountered Velcro on a garment that was held on by anything other than thread.