The voltage drop down to 12.7v after charging is normal. This extra voltage is due to surface charge. The drop down to the high 11s seems high for a 4 GC2 battery bank. The battery bank has a capacity of about 450 AH and you apparently are using about 75% of the capacity. For best battery life you shouldn't discharge them lower than 50%.
Somehow, it seems that a lot of current is being drawn from the batteries. Without having current measurements all we can do is guess what the problem is. To use 300 AH in 12 hours means your average current drain is 25 amps.
