Gothmog????

[Legolas]

As I see it, why would the Witch King have an orc or Black Numenorean as his right hand man when he could have his choice of six Nazgul?

Because they would remain at the tower and be more familiar with the troops (and the troops wouldn't be terrified to death of one of those). Why would Sauron choose a Black Numenorean as his Lt. at Barad-dur? I don't know, but he did - the Mouth of Sauron was no Nazgul.

Okay, Gothmog the lieutenant of Minas Morgul is said to be the second most powerful Nazgul of the nine,

No, Khamul, the Lt. of Dol Guldur was the second most powerful of the Nazgul.