Glad to see you are using a CLAMP-ON AC-DC AMPMETER with your Fluke model.
I use the Craftsman (SEARS) 400AMP (AC-DC) and it really is nice to be able to clamp around a single DC cable to track down high DC Current items... $60 well spent here...
I too think you are a little lax on the size of your generator on what you are wanting to do. I have the Honda EU2000i 2KW model here and if I can turn off everything except the Air Conditioner I can usually start it up but as soon as it cycles the first time it trips my Honda off line... The only reason I have my 2KW Honda is to connect up my Converter/charger unit every morning and do a 50%-90% charge state on my larger Battery Bank. Everything else we want to run when OFF-GRID is run off the battery bank and Power Inverters... Of course this does not include using the Air Conditioner or our high wattage Microwave...
When I see my DC VOLTAGE get down to the 12.0VDC area I know I am approximately at the 50% charge state and then its time to run my generator for three hours to get my batteries back up to their 90% charge state so we can continue on. Going below the 50% charge state does damage to my batteries performance...
We like doing this 2KW generator run first thing in the mornings when allowed to run our 2KW Generator. Camping OFF-GRID here on the East side of the USA sure has alot of restrictions in this area hehe...
Let us know what you finally find out causing your problems...
WE camp off-grid alot and using the Air Conditioner is low on the priority list. Have great luck using the Fantastic Fan and playing games on which window flap to crack open to get the coolest draw of air coming though our OFF-ROAD POPUP setup...
Its all in the planning for us..
Roy Ken