HPWH as hydronic supplement for A2AHP – GreenBuildingAdvisor

Out of nerdly boredom, I have been thinking about trying to supplement my underpowered A2AHP (always disappointed and poorer when the heat strips run for hours on end) in zone 7b with a homebrew hydronic system consisting of a hydronic fan coil, a wee water pump and a hphwh (I can find these in working order for <$500 on marketplace). My thought is to put the water heater in my carport shed (right next to house) where the carport/shed roof has a ton of solar gain. (House roof would be better for larger solar gain but I don’t want to put a water heater in my attic). Heat water up daytime when the shed roof is warm drawing hphwh supply air from the shed sealed roofspace, maybe store more heated water in a spare (available for <$200) water heater tank or two in my coal cellar. Then, run stored hot h2o through the fan coil on cold nights/mornings when a2ahp cannot keep up or recover temp after nighttime setback. Obvi won’t work if I let snow accumulate on shed roof, but this is rare. Shed roof insolation in winter is likely better than 40 kWh/day, so could bank some substantial portion of 10 ton-hrs of heating as mcdeltaT? I wanna say the compressors on those things are just under a ton so that might limit daily accumulation more than insolation? Other than being a waste of money why won’t this work?