I have a Basenji mix also and it took a long time for me to get used to her ways (I spent many nights wondering if I'd made a mistake getting her). It's especially hard if you don't know what you have…the pound said that I had a Collie mix - not so much. One day at the dog park a guy said that he thought she was a basenji, that was it, after reading about the breed everything started to make sense (just as you said about yours). They are very interesting dogs and it takes a lot of patience to understand their nature but it is worth the time.
I use the prong collar on her and it is about the only thing that works - at first I thought it was cruel but after looking at it and understanding the concept it isn't really bad. She still pulls sometimes but when I tug it a little she understands. Using positive reinforcement does work - she really didn't respond to "pack leader" concepts....she does what she wants when she wants ...and that's it.
I am so glad that you've grown to love your girl because not everyone would have stood by her. Rescue dogs are hard enough but if you don't understand them it makes everything worse.... seems like you've gotten to the top of the hill and hopefully it will be smooth sailing from here. Sometimes I think that the "basenji personality" is the reason my girl was in the pound.