Use the 120 VAC element and run it through an inverter.
Ted I am considering exactly what you say I was just trying to maximize the efficiency, knowing that the inverter uses some power
Wouldn't worry about the inverter penalty. If I were doing it, it would be through the inverter with either a mechanical or electrical timer. With some experience, think you could figure out how much stored power you could afford to convert to hot water and still recharge the bank. Then set the timer and walk away. I'm thinking a commercial grade spring driven timer should be able to handle the load.
I can envision a more sophisticated setup that is triggered by bank voltage, runs the water heater, draws the bank down to a set point, then waits for the bank to attain the high voltage set point to repeat the process. Thankfully, those complexities are beyond my engineering capabilities.
Ted