I don't understand that currently. It still has to draw in/blow out air from outside, right?
Come on, a little imagination please
You put the controlled residential ventilation system in the basement, drill through the exterior wall (underground), and then connect a geothermal heat exchanger right away. Sure, the pipes have to go to the surface later to draw in air. But this way, you have the system in the basement and no shaft going up to the utility room to drill outwards there.
Where the heat exchanger then gets its air from can definitely be explained in more detail by someone who is an experienced user here. It was just a thought since you want to put the controlled residential ventilation system in the basement.