One option for backup heat is using a heat pump water heater, a commercial type that can handle the load. The problem with that option is that the heat pump is unlikely to be running at the time I will need it the most, because the outside air will be too low. However, thanks to the 1-day storage capacity, I can set the heat pump to run only during the warmest part of the day, one extended cycle to bring the storage tank temperature up to 140°F, once a day.
Unfortunately, all the water heater heat pumps I found online are designed to work indoor, with intake air temperature around 20C, or 70F. I haven't found the right product yet. The heat pump is an air-to-water heat pump, with intake air temperature as low as 35F.
Another option is to use a geothermal heat pump. The heat pump must be designed to heat water, not air. Most geothermal heat pumps heat air, but there are a few that heat water, such as the water furnace. Looking at their website, it appears they have a design that is suitable for my application: Model 084.
According to the performance table in page 5, the entering source temperature may be as low s 32F, with an entering load temperature of 104F, giving a COP of 3.1. This COP probably does not include the energy used by the two water pumps (load ans source). Instead of being connected to ground loops, the heat pump will be connected to an air to water heat exchanger. There will be a gradient between the water and air temperature, that must be determined (it depends on size of exchanger, and output of heat pump).
The heat pump can be set to run only of the warmest part of the day, such as late afternoon. A simple way to do that is a timer. A more efficient way would include a smart controller retrieving the max temperature for the day from a weather forecast, and start the heat pump when the temperature is less than 5F below the max. The 5F gradient should be determined by the amount of time the heat pump will have to run to bring 270 gallons from 100F to 140F.
The month of December 2012 was colder than average December months in past years. If we assume a 5F gradient for the heat exchanger, minimum temperature requirement is 37F. Every day in December 2012 exceeded 37F at their max. That doesn't mean they exceeded for long enough to heat 270 gallons. We need to make another assumption for that, such as the max temperature of the day should be 5F higher than the min required temperature to provide enough heat (number TBD for now). Minimum outdoor requirement becomes 42F. 11 days were not suitable. For those days, the electric strips will have to be used. Assuming a COP of 3.1 for 20 days, the overall COP for the month is 3.1*20/31 = 2.