Hayden - thanks! That was the thermostat, and I installed it this week. Unfortunately it now looks like the thermostat wasn't the problem after all. I've got a local guy coming to check it out tomorrow. Hopefully it just needs a shot of refrigerant.
As near as I can tell, this is the original system in the boat, so the old Adler Barbour has been chugging along since 1994. I guess it's not unreasonable for it to need some service!