Final result: converted German military bag into pannier. Waxed the cotton twice and treated it with a heat gun to infuse, stiffed the back, and mounted.

I gave the cotton a double wax treatment, to make it water repellent. Stiffed the back with a sitting pad a had laying around, which fortunately fitted exactly to the bag and keeps it from flapping around.
This is a double bonus, since now I always have a pad on hand.