After faffing around with trying to eek the last bit of charge out of the battery, this weekend I decided there _had_ to be something wrong with it. I took it (and a bunch of old UPS batteries) to batteries plus, UPS batteries for recycling and the solar dock one for testing.
The guy put his electric meter on it and read off ~11.7v and announced the battery too discharged to test. I explained the battery had been on the panel for 6-7 hours at this point and so it _should_ be fully charged, he tried to tell me that there was no way the panel would have it charged that quickly but quieted down when I said it's a 100W panel. He then went into the back to see what his fancy charger would do with it. He came back saying his smart charger refused to charge the battery as the charger thought the battery fully charged and he didn't know what was wrong with it, but something definitely wasn't right. So I plumped for another battery the same.
Last night, we had friends over and I put the lights on for several hours. They behaved well, and looking at the over night logs, minimum voltage was 11.8v and there was no dropout. When I reconnected everything I connected the light controllers to the "Load" connections on the controller, these have undervoltage protection and will cut off at 10.8v the main controller is connected directly to the battery so that it will only drop out when the regs fail at about 6v (at which point the battery is _done_)
On a side note, you know what's cool? when one of the visitors mentions that the lights are cool and asks where you go them from and suggests Amazon. Your answer of course is that they came from there (and point to the lab)