The gen is rated well above the capacity of the A/C and is evident that it is capable of easily handling the load(s) in eco mode as it only rises to 3050 RPMs from 2650 RPMs and does not go into overload. I don't usually do it so as to ease the load on the gen but, with the gen in eco mode, I have had on the A/C, microwave, coffee pot, and electric water heater all at once. The gen did kick up to full throttle speed (3450 RPMs), but it did not go into overload.
If the issue was happening in reverse, that the gen would go into overload when running on eco mode but would handle the A/C compressor kick on in full throttle mode, I would agree with the "hidden" usage idea but since it works fine at the lower eco mode RPM it must be something with the gen advancing when in full throttle mode, even though it should not, that is perhaps causing the overload.