Welcome to the forums.
I have to agree that reading about a basenji is a lot different that living with one. Cody is my first dog (besides the ones that I grew up with as a child and teenager). I got him a year and a half ago when I was a senior in college, and I just knew that I was ready. I had done the research, understood their good and bad sides, was aware of their little quirks, and I was pretty sure I could handle living with a basenji. Let's just say that it was quite a struggle at first. It's one thing to read about the destruction they cause, but it's entirely different when you come home to shredded blinds, holes in the carpet, chewed window and door moldings, pots and pans pulled from previously closed cabinets, plants knocked over and soil trampled into the carpet, etc, and there's your beloved basenji, innocently sitting amidst the chaos. BTW, that was all in less than 20 minutes… I had left him to go exchange his crate for a larger size. He also decimated my wardrobe that first year, and still has an affinity for jeans, bras, and zippers. Luckily, the training process works both ways... I have been trained to pick up my stuff if I don't want it destroyed, because if he can reach it, it's fair game.
I'm not trying to discourage you from getting a basenji; I'm just saying that spending time with one or a few will give you a better perspective. I think fostering is a great idea. You could try posting something on craigslist about hanging out with someone's basenji. In hindsight, I wish that I would have spent time with a few. If you weren't so far away, I'd let you "borrow" Cody for a weekend (well, as long as Cody approved, that is).
You also mentioned getting a dog to keep you entertained. Basenjis are independent. While you may laugh at their antics (I think they are better than television!), they kind of just do their own thing. With Cody, sometimes he wants to play with me, but most of the time he's perfectly happy entertaining himself. They aren't really out to please humans. I'm pretty sure Cody thinks it's the other way around: humans were put on this planet to do his bidding.
Along with BRAT, keep checking out the "Rescues and Homes Needed" section. Quite a few people will post basenjis that they come across on Craigslist and Petfinder. There are also a few responsible breeders on here that are rehoming basenjis, although none that I know of in the Carolinas.
Welcome again and good luck!