Illustration 3 -  Here, we have a Spherical Projection UVMap and it's the last of our "3D" choices of UVMap Projection Primitives.  Still, it's a no-go as artifacts are still present.  HOWEVER, in the Flat Projection UVMap along the z-axis, there aren't any artifacts!  Could this be the solution to the problem?

Cylinder 5) Remapped -Spherical Projection
Cylinder 6) Remapped - Flat Projection, z-axis

Illustration 4 - To explore the possibility more, I chose the other axis of projection as well.  ALL yielded good results with no artifacts.

Cylinder 7) Remapped - Flat Projection, y-axis
Cylinder 8) Remapped - Flat Projection, x- axis

(cont'd)