From a H356, Story of insulation problem I ran into while cruising to the Bahamas.....
one picture got left out.. shows the area below the sink
I have the same boat... And have had the same sweating problem. Others have had the same. Shortly after closing on my boat I reported this to dealer. The dealer flew someone down from the factory and he totally redid my freezer box and the lids, Lid seals, lock down latches etc. He said that this was something that had been over looked when my boat came off the line. He apologized saying he remembers my boat, this is because he was in the middle of going through the list of things to do get done when he was pulled a way from my boat and someone else was supposed to finish it up but didn't. He even showed me a trick on how do double or triple seals on the lids by using plain old refrig/freezer sticky backed gasket seal rolls you can find at your local Home improvement store.
Your boat was probably coming off the line in Florida while he was down here rebuilding my freezer. My freezer is very well insulated but at -14 Degrees in the freezer even the exterior of the best insulated bulkhead will sweat I guess...I once put ice into the bottom the of the freezer . It took nearly a month in mid August to get rid of the ice it froze to a solid block even the drain was blocked and frozen solid a good 12"-18"s or more inside the drain hose to shower sump. Had to finally use a heater on the drain hose to unplug it and inside the box to melt it all out it. Ever since then ice stays in the bag.
I always leave the cabinet door under the gallery sink open and the cushion seat back gets propped up when I am not there. If you do not want to leave the door open when boat is not in use you could install a louvered teak vent in the cabinet door with a small fan....In any case this solved it for me. I have found good ventilation is the key in these areas. I would remove the bubble wrap off the wood under gallery and let it breath and dry out otherwise it will stay damp and rot.