So how do I calculate this? Obviously my approach failed miserably.
I'm not sure what you are trying to calculate. Here's what I think you should try to calculate.
First, how is your basement currently conditioned, and what are the conditions? If it's 68F and 60% RH and maintained that way by passive heat exchange with the upstairs and a dedicated dehumidifier, then it's worth thinking about how much dehumidification the heat pump water heater will provide. That will provide the benefit of not running the dehumidifier as much, and reduce the sensible cooling provided.
Then, if it's heating season, all the heat that goes into your water heater will have to come from somewhere, so it will be an extra load on your central HVAC. If your central HVAC is a COP 4 heat pump, then worst case the water heater nets out to COP 2: the heat pump uses 1 unit of energy to move 4 units of heat from outside to inside, and the water heater units another unit of energy to move those 4 units of heat from inside to the water.
On the other hand, during cooling season, it's going to reduce your cooling load. So it's worth considering how many heating degree days per year you have versus how many cooling degree days per year you have in your climate (and forecasting how that's changing over the next 10 or 20 years).
This discussion is based primarily on a model where heat exchange between living space and the basement dominates over heat exchange between the basement and the earth. But if your basement is not well thermally insulated from the earth, or is well insulated from the upstairs, then one would need to consider how that changes the analysis.
Cheers, Wayne