We have a 1990 Winnebago Micro Warrier, and unit came with a WEN 2350 Inverter. It is stored in the same compartment as the original one and can run the AC without an issue. However, our AC has a "start capacitor" that minimizes the power load when you first turn it on. This whole setup is about $450 and plugs into your standard shore power.
I have not priced all the options, but intuitively, WME seems to have the right idea with a 12V system. In order of preference for me: 1) 12V system 2) ONAN replacement generator and 3) Inverter-style small generator that you can take with you. As a bonus, when we lost power at our house a few weeks ago, we fired up the 3) generator and used it to run our refrigerator while the utility company fixing the problem.