I have an ef2400i also. what you described is spot on to what used to happen to me. my cure, 1 is to always use sea-foam in my gas. that alone made a big difference when I couldn't get alcohol free gas. 2 when you have to use the genny for a/c first make sure any side loads like electric h2o heater or fridge are on propane. then turn a/c fan to ON followed by turning on the a/c to cool. this in effect, ramps the genny up prior to a/c compressor kicking on. you could put the delay timer in the system, but I never had to.
BTW, those parasitic loads won't necessarily ramp up the genny from idle. I've been using my Yammy for about 5 years now without trouble.
2000 Cherokee 29BH with 6V batteries, LED lights & 400 watts of solar power, flipped axles and raised. 2007 Tundra 5.7L DC-LB with lots of mods. C-co, 8/158th AVN Maint.