This is not an answer for your hot water, but I would like to briefly explain about time of day metering; we call it time of use (TOU). If I buy electricity in Asheville, NC (my home) at the normal rate, I pay $0.085/kWh in the winter and $0.095/kWh in the summer. But on the TOU rate, I pay $0.059/kWh on-peak and $0.045/kWh off-peak and $3.73/kW in the winter and $5.02/kW in the summer. I have a demand controller to control by on-peak kW. I bought a 105 gallon Marathon and heat it off-peak only. This means I use only the lowest price electricity for heating my water. I have saved $1400 in the last 17 months on my electric bill.
Some utilities have TOU rates but don’t advertise them. In order to get low utility bills you need to know utility rates, appiance efficiencies, and how to convert between kWh and BTUs. Then when its time to buy the next appliance you can choose the one with minimum cost over the life cycle.