Unable to add the specific draft to the extruded feature

I need to extrude a complex 3D surface to another even more complex 3D surface, and the extrude must have a 10 degree draft. The result must be solid.

Lofting/Boundary is out of the question, as I need it finished still this year

...But the draft doesn't work (works only for a small segment), as visible on the pictures

Adding extra segments goes shenanigan mode

Although the source and destination surfaces are complex, the problem seems pretty much like another SW's fussiness

SolidworksParts And Features