I might suggest trying Tenacious Tape from McNett before you do any stitching. I haven't ever tried it before, but its extremely adhesive and is basically about 2oz ripstop nylon with an adhesive backing. I've used it for other repairs before and it is many times better than duct tape. If I had to repair my hammock, this is what I would use.
In the words of the Great Mackey, "Never lose your elevation!"