Hi Zooen,
not sure if this method helps to create the spiral path you need but it does hit all the circle positions you show in the 2D.
Basically I created the Hour glass inner shape and projected the 2D connection lines onto it (front lines then back lines) joined up the results to create spiral.
Duplicated it and rotated 180 thus getting the 2 start spirals needed.
Cheers
Barry
Added Final image.