Crunching the battery case in the bench vise, plus a bit of screwdriver prying, did the trick:
Peeling the case off revealed the eight lithium cells and the protective PCB:
As you’d expect, each pair of cells has an individual contact to the PCB for monitoring and equalizing, which simplifies connecting the battery tester.
The case emerged from its ordeal with only superficial damage, so it’s now back in the laptop to fill up the slot. I tucked the PCB inside, although I doubt I’ll ever rebuild the battery with new cells.