Several dry campers we know including us have installed the easy start on 13.5K BTU AC units with very good results. However I will point out one thing to consider regarding the honda 2000 and the easy start. The honda 2000 engine is pretty much max'd out so output max power goes down with altitude. We found that around 3500ft density altitude the 2000 is likely to overload, luckily the easy start just shuts the AC down for about 5 minutes rather than having the honda completely kick out. This is with all other 120V loads including the converter power turned off.
solution honda 2200. it has a much larger engine and even at 8000+ft it can run the AC unit and still have about 300watts to spare. As a check with a honda 2200 we ran our AC at around 8000ft in 100F temps and I turned the fridge on AC just to see what would happen, 2200 kept on running, no overload.
Before the easy start I was lugging around two honda 2000's, paralleled for AC, when the honda 2200 came out i bought one, gave one 2000 to our son, and for a while carried around a 2200 and 2000 as a "just in case" for AC when boondocking. Gave that up, never have needed more than the 2200 even at very high altitudes. Solar charges the batteries,