Ok, I decided I'd try my 14V cordless drill battery charger on them, as that seemed to be close to Mark and Stew's recommendations. I tried to hook it up, and the charging light would come on for five secconds and fade away. At first I thought this was because I wasn't making good enough contact, but eventually discovered that it was just what the charger did.
At this point, I threw it back in the fluke, and plugged it in, and it started to charge. Had I left it hooked up long enough for a bit of charge to build up? Had the higher voltage shocked the dendrites out of it? Did I just get lucky and it decided to work again? I'm not sure, but I've got a few more of these to try, so I'll let you know if it's reproducible.
Matthew