Coming late to the dance, but here is my two cents,,,
I have a lttiile frigidaire 5k BTU unit I run very rarely. I run it on my eu1000 Honda genny. I sue the slow start method, run the engine on full throttle, no load, turn the fn on and let it spool if full for a few minutes, then turn the compressor on low. The Eu100 will barely start it,, but runs it fine. It draws ~550 wats running.
My guess is that you are going to be REALLY hard pressed to get any meaningful run time off nearly any 12 v battery set up. Even if it would run it, my guess is that any inverter will drop out due to low voltge shut down first. You could start it on the genny, and the a quick switch to the battery while the compressor is still running, then leave it running full bore so the compressor never shuts off.