Adjust surface seam based on uv point

How to adjust surface seam based on uv point?
I try this but it is not accurate

surface (18.2 KB)

I thought this is a matter of aligning the base plane of the cone…

The cone is aligned to the Y axis of the base plane. This does not make sense to me.

Extrude to point works like expected and the seam is in the XZ plane of the base plane.

surface (23.5 KB)

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I replace the cone with Extrude to point surface

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