Hi Dan,
I don't even really have a 110V system on the boat anymore. Some parts of that system were getting suspect and I've taken most of it out, other than a battery charger.
I plan to run the heater and dehumidifier direct off the shore power as you suggest. I will also probably buy a 12V battery charger and use it to keep the boat's 12V system topped up. I'll buy a cheap 12V battery and use that as the ship's battery, totally disconnecting the current high-quality ships's 12V batteries. I learned the hard way in Spain 10 years ago that using a battery charger to keep deep cycle 12V batteries topped up, never letting them discharge, causes sulfation. Fortunately I was able to salvage them, but this time I'll just use a cheap sacrificial battery.
Thanks,
Max