> Any ideas on how to avoid this problem in the first place?
You'd probably want to have a smaller piece for just the thread, so that the part that's spiraling around doesn't run into itself. Surfaces that cross back over themselves (even just barely grazing) will tend to cause a lot of problems with intersection calculations.
So for example you'd want the inside part to be just a straight extruded cylinder surface and not a spirally type thing in that spot.
