Stepper motor creates voltage spikes in Due

MarkT:
You've not shielded the wires from controller to Due?
You've run the signal wires near the supply or motor wires?
You're wires are random and not nicely bundled as twisted pairs or equivalent?

I think a photo of the layout might help here...

Correct. Unshielded stranded wires. Bundled, but no twisted pair either. Obviously the signal wires are near the motor wires, the terminals are right next to each other.

Are you suggesting the signal wires pick up stuff from the motor wires? Keep in mind, though, these effects are present even if the motor is not running (but is electrified). In this case I would think there is no current present in the motor wires, and therefore nothing can be picked up?

Please see attached picture to get an idea of what kind of wires I used. This is quite messy, though, the problem is also present if the wires are laid out more nicely in an ordered fashion! Also, the screw shield has no influence on the issue, I tested that as well.