That is precisely what the splined lug nut was/is. The problem was conventional hex lug nuts would not work as the socket (yes, thin wall) would disengage from the nut (because the nut was too short) before it would tighten against the seat. This was because the hole in the wheel was too small of a diameter to allow the socket to enter. In other words, the socket hit the wheel before the nut bottomed out. Thus, the exercise of finding the splined nut that would work, which I did find for about $27 (no tax or shipping), including the fitted spline socket, for a set of 20 (intended for five lug nut autos, like the sets at Autozone) even though I only need 16.
