About the Champion, had mine for 3 years, happy with it.
#1 Be careful with the remote start because you have to leave the power on to make it work. It will kill the battery, I've been through 2 now. Added a little solar panel to keep it charged.
#2 It does not run in eco mode powering an AC. Yes, you may have the switch set to eco mode, but it automatically goes into the full power mode if the draw is more than eco mode can handle.