8 cells (280Ah each) would give you 2 x 280Ah @12V batteries, or one 24V 280Ah battery. Energy in both is the same: 7 kWh or thereabout, compared to 2 x 1.2 kWh for your BBs. If you make it 16 cells, you can go 48V 280Ah, for around 14kWh of storage. Or 2 x 24V or 4 x 12V with these 16 cells - energy stays the same.
To run an AC, how much does it draw? Suppose you have a 1kW load (continuously), 8 cells could run this for about 7 hours (not including inverter losses, it will likely be closer to 5-6 hours). If you have a 3kW load, you get 2 hours. Double the cells, double the runtime. The higher the load, the higher you want your battery voltage to keep the current low (P = U x I).