Mark
May I recommend that you simply replace the screening material. At the harware store you can get a screen roller tool and new fiberglass screening plus new rubber splines. Pull out to old rubber spline in the existing screen frame, cut screening larger than needed. Use the screen roller to push the sline into the groove holding the new screen into the srain less frame. Then once all around, cut excess screen with a utility knife. Finished.
That's how we service our screens. It's not that hard.
Hayden