Question

How did the founders solve the problem of a too powerful military

Answer 1

With the goal to prevent a military that could run the country through its own fire power, the founding fathers came up with a single and elegant solution.

The military in the USA is run by a civilian. Obviously, not any civilian, but the one in the highest rank of the executive branch. So no matter how important your rank is in the armed forces, the President of the United States is the one calling the shots.