the PVA MIGHT be viable. Before I committed the airframe, I think I would build a test rig, a frame of balsa, and apply a piece of the fabric by glueing it around the edges. Keep it as taught as you can. Once the edges have completely dried, tried "painting" it with pva cut 1 part to 3 parts water. Brush it on LIGHTLY allowing it to dry between coats. See what happens. If it tightens the fabric put doesn't crush the test rig, it might be worth a try. Putting a bit of talc in the first couple coats might be worth a try, too, to help fill the weave.

Post back and let us know how this worked....