The "ice box" on some boats I've owned were very large to accommodate a large quantity of ice and less attention was given to the need for efficient insulation. From what I have read this was the design philosophy on the early Freedoms (like ours). My Allied Princess was the same way. I took advantage of the extra room to install insulation inside the box. I took construction foam (which was compatible with epoxy resin) and glued in several layers and then glassed over everything to make it water/air tight. This reduced the volume of the box but left a very usable amount of space for cruising considering there would not be tons of ice going in there. I got by with a little Norcold ice box conversion unit.
BTW when I first installed that unit without the extra insulation I was having that same defect. It was running 24/7. A friend of mine noticed a big rectangular patch of water beading up on the outside of the boat and yes... that was condensation where my little Norcold was trying to reduce the temperature of the greater Pensacola area! Also the lid of the box was cold to the touch and I had to add insulation to it and create a step with air seals on both. Even so I would double up a beach towel over the counter top with the lid and if you stuck your hand under that towel you could feel the cold.
George