Well, I think I figured out what the problem was. My battery had died a number of times in a row, about 7, since I got it a month ago, from a twig holding the antenna open. I only drive it once or twice a week, since I take the bus to work, so it would be a few days before I noticed the battery had died.
So when I went to start it, I was late to go somewhere, and I had mostly been jumpstarting it rather than trickle charging it. When I went to connect the charger one night, the cells were all low on water. I filled them all back up, connected the charger, and let it run all night and shut off automatically. It'* been fine ever since. I still only drive it once a week, but water in the battery combined with trimming the bush by the antenna so no twigs get stuck seems to have worked.
I'd give you the readings between the terminals, but my voltmeter isn't good enough to check across the terminals. I almost welded the tester to the terminals while checking.
When I checked it before, it was around .037, which is good enough for me. Unless it dies again, I'm not going to fuss with it. Thanks for all your help though