I turned the laptop over again, and played with the battery release. There was no spring action, so I looked at the mechanism and deduced that left was the open position and right was the closed position. I slid the release right and inserted the battery again. It went in with a satisfying click.
I tried to slide the release left, to double-check that I could take it out again, but it wouldn't budge. I went looking for the original manual and couldn't remember what I'd done with it.
I turned the computer right-side up, powered it up, and went online. I found the repair manual for the V6000 on the HP site. The battery replacement instructions were to slide the switch left for removal, insert the new battery, and then slide the switch right to lock the battery in place. Crap. The way I'd inserted the battery, it was in a Roach Motel.
Unless Dr. Who loans me his sonic screwdriver or some kind soul tells me a way to get the battery out without breaking anything, this is the last battery the laptop will ever have. Fortunately, it's behaving pretty well, and I do like having the screen up a little higher.
Even so, using the laptop for an extended period, as I'm doing now to write this post, still stresses my wrists, neck, and upper back. And I don't especially like carrying the extra weight of the 12-cell battery. But at this point, it's stuck -- and so am I.