This sounds too much like I found on the first night of a North Channel trip last year. I was plugged into shore power with no appliances or lights on except the standby mode of the FM cassette deck. Around 2AM I awoke to the tell tale tones the radio outputs when the batteries go dead, yes I did this before but with previous batteries and other circumstances.
After checking the obvious circuits and narrowing it down to the cabin circuit I traced the wired down and found a very hot auto quality butt splice in the head. A fire would have been next as the fuse was not blowing and the resistance was huge. Before I found the cause I was watching the volt meter drop visibly whenever I turned the Cabin switch on, dropping one half volt in a couple of seconds. Needless to say, I pulled the butt splice off the wire and respliced it properly the next day.
So that's my tale and hopefully your solution might in the end be as simple.
Calliope Catalina 30