@escapeartist said:

The cylinders were only 2.5" dia. and the radius was only 1/2".

And whatever faces after these small specs would have about 1/16" edges (in those "turns"), SU will always have problems with creating. Thus TIG's advice.

Mostly we encounter such problems when using the follow me tool or intersecting geometry (with the line tool itself you'd probably not draw so small items) so this is when it's very apparent however it would be a general problem.

Ya, that's what I used to unfold the cone.

It didn't do it in this simple model, but in the model I'm working on, the texture turns black after making it unique and the "texture" selection is unavailable from the right click menu.