[rickst29]

Unless you're running the fridge on 12v in camp (and you absolutely shouldn't do that), your battery should have held up through the night, with maybe 10-20Ah of total power loss during the night. At 12.6V, you started with about 90% State-Of-Charge, and that voltage (as a resting voltage, not immediately following charging) was just a slightly low target - you want the battery to be around 12.73 (at 25 degrees C, it varies with temperature). With lead-acid batteries, it is desirable to keep them at 100% State-of-Charge for the maximum possible amount of time. The charger running at around 13.4V will be fine, if given lots of time for the batteries to recover. It will not be capable of overcharging the battery, because there is a "hump" of about 0.7 volts which the charger must overcome, in order to charge Lead-Acid batteries. The current and power from the charger (into the battery(s) will drop to almost zero, when the batteries have reached 100%.

The inexpensive Walmart 'deep cycle batteries' are actually combination batteries, attempting to balance the goals of deep-cycle use and motor starting use. True "Deep Cycle" batteries are built with fewer but thicker plates, while 'motor start' batteries are built more but thinner plates. The Walmart batteries should not be taken below about 12.15 volts, 50% state-of-Charge. Having been pulled down to 6.5V is pretty bad, but it might be recoverable, to some degree.

If you were NOT running the fridge on 12v from the battery alone, there is likely something wrong within your TM.