There are a group of us that have installed switches to run a 15K Dometic unit off the inverter.
We first installed MicroAir Easy Starts. The Easy Start drastically reduces the locked rotor amp draw when starting the compressor. If you don’t install this...then you’re really gonna need a bigger inverter.
We are using the stock Magnum MS2812 PSW inverter that came with our coaches.
We have all-electric coaches...so our batteries are also powering a Whirlpool Residential fridge.
So, with 928aH of storage...you can run the Air Conditioner for about three hours. That’s the batteries working in harmony with 1,440 watts of solar. And not dropping below 50% state of charge.
We found while driving (this is in a Motorhome) the bi-directional relay will close and share over 100 amps of Alternator power to our house bank. We can actually run the rooftop air off alternator+solar while driving. So, it was a benefit. But, we have to keep track of inverter temperatures. It is a big load on the inverter.
If you go with 15k rooftop air...I would say the Victron 4000 Multiplus would be a great Inverter. At high amp loads...LiFePO4 batteries have a lower Peukert factor...so, you aren’t loosing storage as heat waste. 1000 aH of LiFePO4 would be a good bank. So, long as the nights cool off where you are.
2000 watts of solar... two 1000 watt strings on Networked Victron MPPT Smartsolar Charge Controllers.
If it were me...I would try to find a place on the fifth wheel to mount a mini-split. They are so much more efficient. You could basically half the energy requirement. Unfortunately there isn’t really anyplace to mount one in our Motorcoach. I have seen them on travel trailers, fifth wheels, and truck campers though.