Depending on the bucks, you may want to get several bids from consulting civil engineers. Before you do that though, figure out your EVPI.
Then, if your EVPI is less than the lowest bid it's trial-and-error time.
Mud-jacking may help.
If you can post alternatives, their cost, and the likelihood of each of solving the problem, it becomes a solvable math problem - i.e., decision making in the face of uncertainty.
According to this gentleman,
listing all possible options is the first step, and that's not as easy it sounds.
I have a customer with the same problem; the soil near his house is eroding and his basement floor is already showing a substantial crack, with uneven edges. For him, a very costly 20' high retaining wall is probably one answer. I doubt he can sell his house in that condition, not that he wants to.
The front door of another customer's house no longer closed properly, it turned out for similarly costly reasons. She had to get her front basement wall reinforced with some serious I beams.
Speaking of which, is the stump pit only under your garage "footprint" or is it more widespread? You need to find nearby soil with stable & predictable characteristics.