Hello, I'm going to take a crack at the reversal. I can tell you know a lot .. but for the novice reader I state what you obviously know. First I thought you were kidding but I did eventually think of something. When replacing LION batteries in a flashlight. They often suggest you replace them in a set. Why is that? its because batteries are not identical in capacity. Batteries made at the same time in the same factory are very close though because the chems and mechanicals are identical. That's not true if you buy 2 Rayovac Carbon and 2 Amazon plain label carbon. The Rayovacs will deliver 700mah and Amazon will deliver 500mah. (You know where I'm going ... it just didn't come to mind). I turn on the flashlight and let it run. Consider the discharge cycle on that. The weaker batteries discharge to zero first but the Rayovacs keep delivering current in the same direction. As a result the Amazon cells begin to reverse charge. until the voltage matches the Rayovac. So in your case, if your cells weren't equawl (or didn't remain equal once you began reverse charge) That could expalin it. I wouldn't expect the net voltage to be 12ish anymore, but I hope it helps your own though process. Kind Regards, -Dan-Thanks for the info, but it didn't answer my question. I have quite a lot of experience in reviving batteries.
You can get more information, for example
There is also some useful reading here
US5652497A - Reconditioning lead acid batteries for optional use in a reverse operational mode - Google Patents
A secondary battery, such as a lead-acid or Ni-Cd battery which is normally operable in a first operational mode is treated for operation in a second operational mode. Thereafter the treatment can be effected again so that the battery can be operated in a manner similar to the first mode. This...patents.google.com