Beenthere is correct that the half fan rule doesn't need to be considered here as your fan flow is so much more than the natural ventilation.
Your estimate of $1 per hour is correct.
A naturally drafted hot water heater, no fan for the exhaust, is the most susceptible appliance in a home. Your 800 cfm could depressurize that area by -25 Pascals, almost 10 times what a water heater can tolerate. One option would be to replace the water heater with electric or sealed combustion, like your furnace. Or a heat pump water heater, basically electric.
The other approach would be a damper to allow 800 cfm return air controlled by the fan. That way the damper remains closed until the fan is turned on. But some calculations might say, the damper would also need a fan.
The basic problem is the replacement air has to come from somewhere, either you provide it or the house will through all of the leaks.