Michael,

Well thanks for the detailed clarification!

This is something, I guess, happens so seamlessly that I never noticed it.
In fact, it was a planar line, and I was getting this bold, white colored guide line that was acting unwieldy. That's been a sign that the line was being extruded in a direction perpendicular to the current ortho view.

I definitely think that moving a non-planar curve according to it's "best-fit" normal direction is the way to do it. So very good then! :-)

And there is always the [Set Dir] button.