Roger – I believe there is a slight flaw in you last paragraph
(it just takes about 4 times as much time to heat the water). It seems as though something is missing here. If that were true, then we could use one watt of energy and given enough time have all the hot water we want.
Using a little logic/common sense because I don’t have training in this area:
When we cut the voltage in half we have to decrease the resistance by one fourth in the heating element in order to create the same amount of energy/heat.
Now let’s assume the 240v element is designed to operate at 440 degrees in order to heat the water to its desired temperature in a reasonable amount of time. A thermostat will shut it off and let’s assume that is at 140 degrees. Now using a 240v heating element with 120 volts will give one fourth the amount of energy/heat that 240 volts does. One fourth of 440 is 110. A heating element operating at 110 degrees will never heat the water to the desired cutoff temperature of 140 degrees.
Now my thought process could be wrong, so if it is tell me where.
Dave 
www.tolandmarine.com