The only way to cut generator recharge runtime. While still using the same amphrs of power is to use a bigger charger/converter that can supply more amps up to max amount the batteries can absorb , replacing 200ampHrs with 270Ahrs, might allow you that third night with heat, but it is Not going to shorten your generator runtime, replenishing the planned for battery ,
capacity , replacing what was used the night before, will require the same amount of time. Unless a stronger charge system is used
I'm assuming that you think that with a 70 amphrs increase, you have a buffer where you can run the generator less and not go back to full charge on Day #2 and #3, and still have n enough battery power for heat on night #3,
You have not provided info to show this is possible,
How many amphrs is used overnight, how many amphrs will a 2 hour or 3 hour charge return to the batteries,
Do you have a battery power monitor that will track battery capacity , track power out and back in , show you the "state of charge percentage" , the amphrs remaining in your batteries