If I understand your problem correctly, this can not be solved by only a variable section sweep. The geometry must be created in steps.
In the first example (spiral_03), the distance from center to center is defined by a point along curve pattern and is measured along the main surface. The spiral is defined by curve through points. The points must be selected manually and the option to place the curve on the surface can not be used (too slow and the spiral can only partially be created). Once defined, the main geometry can easily be redefined.
In the second example (spiral_04), the distance form center to center is absolute. The spiral is defined coil by coil. The distance is defined by the intersection of a circular sweep with the geometry. Each coil can easily be created using the copy, paste special option + advanced reference collector.