Here is a picture of the curve segments, blends, and important points.
It is after the fact, after the Blends are done. The midpoints are different from the initial midpoints, but are nearly essentially the same, very nearly. (Two of these final midpoints are slightly off of z=0.)
(Well, the segment labels are for the (deleted) 2D planar segments, but look, very nearly, the same as the Blends in 2D, Top View)
(In this 2D view, everything looks planar, but does have z offsets.) (Initial segments Elevation to z=+A, or Lowering to -A, could be discernable in a side view.)

Blend with Bulge passing through a specific point would be handy. Some sort of optimization routine, to narrow down the Bulge decimals, to nearly match the point?
A little trial and error is easy enough.
A second stage fine-tuning slider might be nice? To capture more decimals. Display could show more decimals?

So that is the algorithm. I wonder how hard it would be to script it?

- Brian