If you are getting measureable voltage it should be relatively simple (which is not necessarily "easy" though it can be) to track down.
The way I am understanding this, you only have this issue when hooked to shore power, correct? If you are on battery with the inverter
on, do you still have the same issue?
Have you tried hooking up to a different shore power outlet to double check it is not a dock
If I understand you correctly, there is only a voltage when the GFCI circuit is energised? If that is switched off at the breaker there is no measureable voltage on the keel? If that is the case, I'd physically remove all 3 outlets, well I guess you could just remove the 2 hot leads and leave the grounds connected but I am a wuss in my mature years and would simply spend the extra few seconds and remove all 3 wires on each and put a fold of electrical
tape over the ends before proceeding. Anyway, switch it back on and see if the voltage has gone away. If it has then start checking out the breakers but if it comes back start looking for some splices in the line that are getting wet. You might have to do some digging and if you can track it down in this direction and locate some offending wires it may be simplest and best to simply run all new wire in that circuit.
Anyway, hope that is a start and post back what you find out.