GCs are normally rated at 230AH, so 2 in series gives you 12V at 230AH. A 1500W inverter can draw 1500W/12V=125A at 12V. Actually add 10% more draw due to losses. So depending upon your inverter loads it won't take long to use 115AH or 50% SOC.
DC charging from your gen will be very very slow. Use instead the AC output to a say 50A multiple stage battery charger. When you want to use high loads like a coffee pot, etc don't use the inverter, instead run the gen and use AC. Then use a much smaller inverter.
Unless you take the batteries home for charging you have another problem. You can reach 85% SOC with several hours of charging. 100% takes many more hours of gen run time. How are you going to accomplish this before heading home? So you either take the batteries home, add solar or accept shorter battery life.