I can't see using more than 15a at a time from the 2000w inverter.
The MW might pull 150a while running on its 15a circuit. The a/c is the only 20a circuit in our trailer. (although the USA version has all 15/20s instead of 15s in the Can version.- I don't know if they have 12/3 instead of 14/3 for those circuits though)
Anyway it should be understood that when you plug the 30a shore cord into the inverter, that is the same as adapting down and plugging into a 15a pedestal for how you do your power management among the 120 stuff. WH and fridge on propane to use the MW etc.
So if the transfer switch is 15a and the choice is Honda 2000 vs inverter, that is all 15a anyway. If Honda x2 like OP has, or a H 3000 then could run a 20a. We have a 3000 but split things up among receptacles anyway, so 15a max on any one.