Hmmm, this has been hooked up like this since spring??
Interesting deal. If the converter is pushing 13.4vdc to the batteries, and it's hooked up "backward" (neg to pos and vice versa) it would seem that 1) the battery had zero charge when installed or it would have blown the fuses at the converter or 2) the converter fuses are removed or bypassed. If they were removed or bypassed and the battery had been at full charge I would still think that you would have experienced some sort of converter anomaly.
Now, getting -6vdc from a +12vdc battery is......different
Never seen it. Just thinking out loud, and probably what you were saying; if the battery was totally dead (empty - a blank canvas so to speak) then connected backwards, over time, then would the battery charge "backwards" changing the polarity of the battery? Interesting. Why not charge to -12vdc?
It's something to ponder but for me I would throw the battery away, get a new one, get someone that knows how to connect it (then double check it) and do a thorough check of the converter. It's a wonder that thing didn't explode.