Stitching a new panel on something that big and unwieldy and heavy will be a dog. Place that works on large boat sails? Maybe that's the canvas shop you mentioned. How about sealing the mesh? If you don't mind the uglyness maybe squeegying a few caulking tubes of clear silicone seal on the panel. Certainly would stick to a mesh. They have that stuff that is UV resistant and it should handle weather well and won't attack the mesh. Could even build up a couple layers from both sides. Just one of my crazy ideas. The world runs on silicone seal, PVC, and electrical tape. Pardon my spelling....too lazy and tired to check.
Al