We've had our gasoline version Champion 3100 with remote start going on our 3rd season and it has no issue whatsoever running our rig's AC unit on very hot days or at high altitudes (up to 8500'), even does so on eco-mode.
You could get the Costco version and see if it will perform the task you outlined above on propane, unless there is something different about this dual fuel model, it should power your rig's AC unit on gasoline mode if anything.
You could opt to go for the larger 3400 watt Champion for added power margin for a bit more $$$, have heard good things about the new Harbor Freight 3500 watt inverter genny that is a heck of a buy if they prove to be durable.
Since we have an onboard gasoline Onan on our rig we had grown accustomed to the simplicity of starting/stopping our genny from within our RV. Seen a deal on one with remote start, and now have over 200+ hours without a hiccup.
