We had a 1992 Award Classic 30. The battery-box and tray was the same as yours.
The moisture seen may just be from dew in the morning. The box is vented to the outside and no insulation. The wires going to the battery box are way to small for today's 3-stage chargers. The original converter/charger was only capable of 3 amps charging. It could still be capable of overcharging the batteries.
We upgraded ours to a 3-stage charger that plugged into the original converter box in 2000. The wiring should be upgraded to a correct gauge if you do that.
We loved the trailer but traded one of our Dodge pickups and the trailer for our current MH in 2006.