Outback is supposed to be working on a really neat feature for the FX/VFX series that's already on the "Grid Tie" inverters: "generator support".
Basically...you run the generator but if any loads need more than the gennie can do, the inverter will make up the difference. This is a killer solution to the "startup load problem" with air conditioners and the like.
In theory you could run a 13,500btu (maybe even a 15k) on a fuel-sipping little Honda EU2000i (1600w continuous, 2000 peak).
The gennie in question will have to be putting out a CLEAN sine wave - the Honda EU series and other "inverter based generators" from Yamaha, Suzuki ("Robin") and the like should be perfect. A Honda EU2000i works out to net almost triple the fuel efficiency of the most economical Onan 4kw gas models (the 1800rpm variants) and even kick the pants off a lot of diesel gennies in the 6kw or above range.
Outback is working on a firmware upgrade for this...installable at the various alternative energy shows they show up at (see the calendar in their forums) or at their HQ in WA state.
Meanwhile, even without that you can pull a trick: the Outbacks can deal with surges significantly past their "cruising power" for up to 20 minutes plus - the 2800w VFX series can drive 4000w for a bit and they autoswitch over to gennie power REAL fast. So you start a 13.5k aircon on inverter power, run the AC at max for about five minutes, leave it at max so it won't "cycle" and fire up an EU2000i or similar. Transition is seamless. You then turn off the Outback completely via the control panel so it doesn't do battery charging and presto, you're running AC for dirt cheap. If you have any solar panels those are still charging the battery and your 12v systems are still up - for computer use or whatever, drive it with a smaller secondary inverter like a $300 Samlex 600w pure sine.
But...when the "gen support" function is fully debugged, this will be THE hot ticket.