Countrymod 12 volt AC problem for AC300

Having watched many You tubers videos of campers adding a energy efficient 12 volt A/C countrymod unit I was excited and envisioned using my Bluetti ac300 to run the 12 volt A/C unit when boondocking or at least while my 800 watts of rooftop solar extended my ability to be off grid. So I jumped in (without full understanding and bought my 12 volt A/C unit) After researching more I realize my original plan of connecting the 12 volt A/C unit to my bluetti AC300 won’t work as I had planned. Alas, I was wondering if anyone had any suggestions to a work around. I still have my roof 110 volt coleman 13,500 BTU unit that I think my bluetti ac 300 would run, for at least a short time. 1-2 hours. But I wanted to boondock, and now that I own my countrymod unit I was wondering if there could be a way to run the 12 volt a/c directly off a separate 400 am hour Lithium iron phosphate and somehow use the Bluetti to supplement the separate battery to extend the life? Or something else/better that I haven’t the knowledge to have considered?

Addendum: from what I understand, the reason the Bluetti AC300 won’t work with the 12 volt Countrymod inverter A/C unit is due to the max DC output 10 amps from the Bluetti AC300. The 12 v Countrymod A/C requires up to 40-60 amp at highest level of A/C usage. Any suggestions for best use of AC300 to salvage dilemma would be appreciated. For example purchase of separate Lithium Iron Phosphate battery to run the 12 volt A/C and possible Running the 10 amp output from the Cigarette lighter to the separate Battery to boost it’s run time? Is this feasible? Any better Suggestions?

I was wondering if anyone had any suggestions. I have an AC 300 power station and I am hoping to use a 110v Higher amp battery charger plugged into one of the 30 amp 110v outlets of the AC 300 unit to charge a 300 amph lithium iron phosphate battery which is directly powering my 12 v countrymod a/c unit and hopefully extend the watthours and the running time of the off grid 12countrymod unit. Could anyone please suggest me what is an optimal battery charger (optimal safe amp charging capacity, brand) to use to optimally accomplish this. But I want to boondock, and use the 12 volt countrymod A/C unit to keep fido from getting too hot while we are out of the camper and off grid. I know that my AC300 can only provide 30 amps at 110volts output to a charger, and I have seen 110 volt, 80amp output DC chargers, but don’t know if using an 80 amp charger would be safe or even the best amperage for this purpose to use. The specs of one of the Vevor DC lithium chargers are as follows: input voltage frequency/100-120V AC/60Hz, output charging voltage: 14.6V DC, charging current 60amps, max output power 876 Watts. Any suggestions would be appreciated