The newest spinwheel design is working surprisingly well. All the fancy math with angles and tangents wasn't completely necessary; the wheel is working adequately with just radii for Inside, Outside and Lock. I did need to tweak the state machine with some intermediate states to avoid getting stuck in certain transitions. The key breakthrough was a diagram I call Quadrant-Chaos, with a lookup table representing Clockwise or Counter-clockwise rotation. A few threshold checks make it function adequately for the prototype.
Occasionally the spinwheel will fail to lock, or skip a state. This implies the angles and tangents approach might still be the final solution in the implemented Construction project. However, the spinwheel is certainly at a solid prototype level of functionality, so the technical risk is mitigated.