you don't have any controller....?

Perhaps your cover is really limiting the output to a safe level. When "full"batteries take very little current. The batteries in the video below were charged via solar and even this very small 12W panel is capable of pushing the voltage over 15V and into the danger zone on a 125Ah flooded deep cycle and a 220Ah bank of 6V Lifelines...

This is what a 400Ah bank of Trojan L-16's need in current to maintain 14.4V when they are full, just 0.1A of current to maintain 14.4V. Raise it to just 0.3A, with the voltage unregulated, and the voltage climbs towards the 14.7V range..