When I saw your question, I thought "goodie, somebody may have a solution."
So, I went out to test your question and ran into a major snag.
I grabbed the tester and have hot skin again. OK, great! I turned off all of the inside breakers and still hot skin! Even when I emptied the water heater too.
Well, back to the drawing board. First I am going to drive a ground rod next to the trailer to get a good earth ground and try to measure actual voltage, if possible.
I am concerned that the meter is screwed up and/or the inverter is not wired correctly or ??
I will try to get back at it tonight and tomorrow. I could live without electric water heater, but not this intermittent shock potential.
Thanks anyway, for now.