TechieChick,
I also live in SE Wake County outside city limits (what part are you?) My covenants say no animals or poultry, except household pets. Most everyone on my end of the street knows I have chickens, but no one cares. I believe that as long as no one can see them, smell them, or hear them - they don't care.
I have 1 acre with trees bordering 3 sides of the backyard. Only one neighbor can see them when they free range, and I did consult with them before I got them. The coop is in the shade under some trees. I even had a HOA board meeting here and no one noticed it out back. Pretty nervy, huh?
I'm am so smitten with them, that I would go door to door to get the covenants overturned if someone caused me trouble. We are not a big HOA and don't enforce much of anything, so I even volunteered to be President. I figured if anyone complained, they have to complain to me. Plus if someone wanted to cause me trouble, I'd have some respect on my side. No one else would take the unpaid job so I'm practically a hero.
So, with a 6 foot fence and nearly an acre, I don't think you would have a problem. Getting the blessing from each of your bordering neighbors would be icing on the cake. The gentle sounds of hens aren't loud, and my one that has cackled doesn't distinctly sound "chicken" from a distance.
Good luck!