Today, I scrubbed the burned fabric with a mixture of baking soda and water, to neutralize whatever might be left of the battery acid. I rinsed with boiling water and left it out to dry in the sun while I went for a ride.
When I came back, the bag was mostly dry, so I finished patching the bottom and sidewalls.
Using doubled-up Thomson stem bags and small, close stitching, I was able to effect a repair that, while not professional-looking, will be strong enough to hold for quite awhile.
I ran out of dental floss, so I switched to a coat-weight, heavy-duty thread tat was actually harder to work with (it kept coiling and snagging). But it should hold up well enough.
I found some old straps to attach the bag to a saddle with (the bag had n't come with straps or a dowel).
I re-attached the pocket strap that was hanging by threads, and I removed the leather-and-metal brand tag on the front flap because I've never liked that style. If I can find an older Carradice patch to sewn on there, I might do that.