As for why NBC let her go on "navel maneuvers" that Barb Eden could only dream of, maybe it was the old racist mentality that Nichols could do it, because it was "expected" of someone who was non-white; we are talking about October of '67, after all. Before anyone protests or blushes, consider this: look at the number of original cast members of "Sesame Street" on NET/PBS only a couple of years later, and you'll see a number of blacks and latinos, who were deliberately selected to stimulate their audience because they would not be seen as authority figures.
Wingsley,
I think you hit the nail right on the head why they let Nichelle Nichols show off her belly button and not Barbara Eden. It's the old "National Geographic" mentality that allowed them to show naked breasts of non-white members of primitive tribes and not the breasts of white women anywhere else except in Playboy and other skin mags.
And yes, I love Uhura, esp. in "Mirror, Mirror"! Like the o.p., I have had the longest crush on Nichelle Nichols, even when she did the fan dance in "TFF." But esp. back in the day, I would've loved to have been a fellow junior officer on the Enterprise and just sit at her feet and look into her eyes.
Red Ranger