The heat pump in basement idea is interesting, but would not work
unless you had some way to increase the surface area for heat transfer.
For example, if you had buried a network of pipes in the floor before
pouring the cement, you could circulate water through there, and then
have it go through a radiator. Behind the radiator you could have a
squirrel cage/centrifugal blower. Your only cost to maintain the air
temp in the basement would be for an efficient water pump and efficient
squirrel cage blower. This could make a heat pump very efficient.

Of course, if you have that setup, it would be much better to simply
use a heat pump designed to directly work with the water or whatever
fluid is in the pipes. That would be a geothermal system.