Long story short, I'm having trouble conceiving how to transmit rotational force into a plastic 'adapter'. Your advice is greatly appreciated.

A handle has a splined plastic adapter between it and an internal spindle which it will turn. The adapter currently has triangular splines inside and out. Outside they mate with the handle, internally they mate with the spindle. However, we find that the internal splines strip relatively easily.

In my naive analysis, I feel that having a triangular section contributes to this failure. In my mind it's a bit like pushing a weight up stairs, the inclined plane means less force is required so ultimately they fail!

In the attached image, I'm trying a new method. Instead of triangular section splines Ive opted for a square sided version. The height is as existing. I've also looked at doubling the amount of plastic between splines in an attempt to increase the shear force required to strip it. As the spindle is currently brass, I feel it will be the plastic that fails first.

Does it work? What's wrong with it? How can I improve it?
Spline concept.pdf