I currently can't sphere/cylinder map this type of chart/cuts

[ggaliens]

I had to back off on my sort of arbitrarily foamy objective ... and go to a smoothed geodome starting with
like level 128 or more and then smoothing a time or two to get up to 200K vertices.

And then I was able to make an "8" on the object (cutting lines) and the resulting mapping obeyed the poles I had setup ... reasonably.

It seems like sphere mapping needs a bit more stress testing (MAYBE). I reserve judgement and will give it another try with arbitrary triangles.