Use a Registered civil engineer in your area or a Licensed Soil Scientist - at least those would be the people to contact in NC. Your state may be different.
The little I know about building on unstable soils is that piles can be driven to increasing depths until the driving force necessary to move them is some order of magnitude greater than the load that the building will place on the pile. Depths of 40 to 60 feet are not at all unusual for commercial buildings.
A public road bridge in my area is build on driven piles.
I know that helical piers are often used for retrofits for residences. I have no personal experience with them. Most of the installers seem to say that theirs are the best
and that all the others are not worth considering. That does not really help in the selection.