I had about a half hour conversation with a guy from Buckeye Geothermal. He was going over all the various options for how to heat and cool the court. There isn't a perfect option for the room considering the floor is on a slab and three of the four sides are the foundation of the house.
What we're leaning towards is forced air cooling and radiant floor heating. The thermal profile of the room is the big unknown. It's going to be 9' underground, so that will help it stay a constant temperature. However, the windows and other space above ground will allow it to heat up and cool down.
The plan this guy put together would allow us to try some things and if we found we needed more heating or cooling, we'd be able to adjust.
All of the HVAC contractors have recommended a single unit just for the court and then 1-2 units for the rest of the house. This guy thought he could do the rest of the house with one large geothermal unit.
