not sure about some of your other assumptions about engine efficiency and electrical equivalent mpg's. gas engines are extraordinarily inefficient compared to electric, whatever the source of power (even coal!)
Yeah, but I also didn't account for any sort of inefficiency in the electric drivetrain. 90% conversion efficiency is a good rule of thumb, and there's one step from house panel to storage, another from house storage to car storage, and one more step from car storage to motors, so you'd only get about 75% out of each joule that comes out of the solar panel. Even adjusting gasoline efficiency down to 20% on average, that's less than a factor of 2 off my first set of numbers. We're in the ballpark, close enough to know it can't fit on a car, and impractically large for a house.