The toroidal helix script of Michael can be modified to produce (at least some of) the cuts.
The number of turns must include fractional turns, like 1.5.
Also negative numbers may need to be entered for one or both of the two radii to get the correct handedness.
Had to run the mod script a couple of times with different +/- radii...
Well, it is late, and needs more investigation...
- Brian