I fixed on a few years ago, but I wait until now to share the result, to be certain it held up. I think it's a permanent fix for pennies and little labor.
Loosen the screen (the glue is old) and reinforce from both sides. Sand well, and mask to keep the polyurethane off the screen. I'm sure a black Sharpie would hide the minor smears on the screen.
Because the screens are flexed into place, a rigid repair, such as conventional epoxy and fiberglass, won't do. An adhesive with decent bonding properties on plastics was required. To provide flexibility, I reinforced the center break with Sunbrella fabric on both sides. For adhesive, I used Locktite PL S40, which has double the bond strength on most plastics as 3M 5200 or 4200 (they are very good on gelcoat, but not much else). I bet Dr. Sails would be first rate.
Good as new.
The result is a flexible, strong repair that has held up for over a year, so far.