you might want to try installing a galvanic isolater. It connects to the ground wire of your AC circuit. Try shutting off the fridge and unplugging the shore power cord for three months or so and see what happens. Since you are leaving this AC circuit on all the time my guess is that is a big part of the problem. Using a meter see if you have any current in the AC ground wire. Your not looking for much in terms of voltage.
Regarding pitting of the lead, it will also pit due to oxidation, I had trouble keeping bottom paint on mine since paint doesn't stick too good to lead oxide. I ground it down to bare lead and coated with epoxy, two coats, then two coats of barrier coat to give it a good base for paint adhesion, then the paint. Has held up very well ever since, around ten years or so.