You are correct - Neutral and ground only get tied together at the power source. Unless you have an inverter or generator onboard this means the neutral and ground never get tied together on the boat. The risk of tying them together is that a bad connection on the neutral could force current onto the ground, potentially through the water back to earth. That’s bad for underwater metals and any swimmers in the area.The local marine shop only had a 2 pole, 30A breaker in stock and they suggested just connecting Neutral and Ground together. I was surprised by this, since everything I read indicated that Neutral and Ground should not be connected on a boat
I’ll add another vote that this is caused by a bad connection somewhere in the negative line. The voltage drop indicates a bad connection, and the fact that the drop goes away when the neutral and ground are connected means the problem is on the neutral side.I installed the new breaker and left Neutral and Ground disconnected from each other. I measured 115 between Live and Neutral and Live and Ground. But with it configured like this, turning on a load such as the LED lamp, resulted in the voltage between Live and Neutral dropping from 115V to ~100V. If it was a higher load, such as a 700W heater, it wouldn't even run and the reverse polarity indicator on the panel would glow.
I then connected Neutral to Ground, and everything works as expected.