Bullet stability has little to do with ballistic coeficients except that the higher BC bullets tend to be heavier and thus longer and thus tend to need faster rifling twists to stabilize.
A .177 air rifle pellet, for example, has a BC in the 0.01 range and due to the hollow tail and heavy nose, they will actually fly nose first when shot from a smoothbore air gun. Try it for yourself if you have a smoothbore BB gun and some .177 lead pellets. They always hit the target nose first at any range.
Making the bullets shorter and lighter worsens the BC but actually makes them more, not less stable.