Just my opinion ...
Skip the built in generator. Get a portable generator. For the money you will save, you can afford TWO 2000W generators that you can run in series. (Buying two of them means that they are easy to carry with enough power still to run an AC.). They do make portable generators that run on propane.
You are paying a big premium for any kind of "packaged" solution, like Bluetti. 400Ah of LiFePO4 batteries and a good quality inverter/charge/automatic transfer switch (get rid of the converter/charger that came with your 5er) like a Samlex EVO-2212, and life will be smooth and easy. With 300Ah-400Ah of batteries, you can easily run the loads you mentioned all night.
If you want to run the AC off of batteries, you will need 600Ah-800Ah of batteries and a bigger inverter.
You still need solar panels and a charge controller. DC-DC battery charger means you can recharge your batteries while driving.