It would seem an inverter running off the batteries while being charged off solar was the way to go. The batteries could cover power shortfalls (like passing clouds, surges, etc.) The solar would minimize the total AH pulled from the batteries, and recharge then when power requirements of the inverter were less then power output from the solar. You would only need enough solar to cover average loads + a little extra to top off the batteries VS enough solar to cover peak loads (which could be 3 to 4 times higher - for seconds / minutes at a time) think nuking something frozen for 90 seconds while the AC is on. Even a simple car battery could support the additional load of a microwave - for 90 seconds.
