Your driving times Will never ever even come close to fully charging a depleted battery.
To get an acceptable lifespan from a battery, it needs to be regularly fully charged. You cannot just have it over in the 50% to 80% range and expect hundreds of carefree cycles. Perhaps a few dozen at most before you are like, WTF!!!!!!!?>!?!?
If I could not get a battery fully charged by what was available to me to recharge them, i would not Be buying a top dollar AGM, as its price does not make it immune to abuse, and chronic under charging is Abuse.
The better alternator might be able to counteract the load of the inverter while driving and cooking, but loads applied with engine off will deplete it and once they get subjected to partial state of charge Cycling, their capacity takes a Nose dive quickly and a prolonged absorption charge is required to try and restore that lost capacity.
Not that I am sold on the positive reports trickling in, but Firefly Oasis sells an AGM which uses 'carbon foam' in the lead plates, and is said to not suffer permanent capacity loss from extended times spent undercharged.
482$ for a group 31 115AH 12v battery, and they are now made in India instead of the USA. So prospective buyer.... beware.