Re: stray current
The RPI is measuring the voltage difference between the Neutral and the ground. With a load on, as UncleWillie stated, there will be a voltage drop in the neutral leg. The RPI has a voltage threshold between the ground leg and the neutral and the longer the neutral wire and hence more voltage drop, the more likely you will get an RPI indication the further you are away from the panel where ground and neutral are connected. This is why power at the beginning of the dock works fine. I don't think you have a safety issue but a voltage drop issue. Would be interesting to pull your boat into various slips and try it.
The RPI is either an LED or a Neon Lamp in series with a 25K resistor.
5 volts on a Neon will not get it to strike over.
5 volts through 25K yields less than 0.2mA. LEDs would like to see more in the 5-15mA+ range to look like they are ON.
Under normal room lighting, most operators would not even notice the glow.
None of this explains the complaint that all power disappears from the boat when the RPI Illuminates.
Dropping 15 volts down to 110 volts would strain the appliances, but not likely stall them out.
The lights would still be ON, slightly dimmed in any event.
Scoflaw, you're killing us in anticipation of the in Marina measurements.

How bright is the RPI when it is ON and what type of lamp is it?