I may have mixed up U and V. Whichever ramp turns into a nice eyeball texture, that's the one you want. 
That is a wonderful tutorial you found; one of the best I've seen for eyes. The procedurals do add complexity but I think the flexibility and ease of control you get makes it worth it.
The whole thing about rotating the sphere 90 degrees has to do with the fact that the tissue of the eye all flows in that direction. Any subtlties you add to the eye (like veins or texure in the iris) will behave better when the poles of the sphere are located at the center of the iris and the back of the eyeball. Otherwise you'd have textures warping around the poles, and that would be visible if your character rotated its eyes an extreme amount. (For example, if it looked downwith eyelids wide open, the pole at the top of the eye would be visible, and the veins wouldn't look right.)
Finally, remember that the center of the pupil is completely black/transparent, so if you put a pole there it will be completely hidden--which is always good.
Hope it all makes some sense now.
-Steve
P.S. Unfortunately I can't view your scene (different versions of Maya), but your setup sounds like it should work fine.