I would make the test simple and use the 120vac light bulbs on your boat with all the complicated stuff like battery
chargers off. Turn on one light bulb at a time and see if the 120vac meter continues to drop. If you see a decrease in voltage with an increase in AC loads like light bulbs, it could be something simple like a loose terminal connector or screw to your AC power panel or any connection between the meter, plug
, cords, etc. If you use light bulbs for the test, you should see the bulbs get dimmer as the load increases if you have a bad connection. 60 watt 120 volt bulbs only draw a half amp so it would take several to be as many AC amps as your battery charger
uses .This test is better than sacrificing your charger
until you discover the bad connection. Be careful and disconnect your shore tie connection when you get to your panel connections.