So I picked up some 4/5 AA cells from a nominally reputable supplier and popped a pair into the NP-FS11 case from the oldest pack.
All eight cells were within 3 mV of each other, so I sorted them by voltage and picked two from the middle of the lineup. Shorting them together in parallel produced a few microamps of current, so they’re as well matched as seems reasonable.
Rather than attempt to solvent-bond the case back together, I wrapped a layer of Kapton tape around the whole thing. The case doesn’t have quite enough meat to bond, anyway, because the width of the slitting saw turned that much plastic into dust.
A bunch of cutouts along the bottom edge key it into the charger, so I cut out the tape over those sections. Despite what it looks like, the small metal tab between the two terminals (on the top) is not covered in tape; that’s the snazzy InfoLithium contact that tells the camera that this is a valid battery.
The camera reported the pack had about 15 minutes of life remaining, which makes sense given that the cells spent quite a while in transit. I ran it down to empty, put it in the charger, and it seems to be perfectly happy. I’ll do a capacity test after a round or two of picture-taking.
I doubt the tape will prove to be a permanent fix, but as far as the camera is concerned, that slick Kapton makes it go in and out like anything…