One thing that MIGHT help is to really exercise and wear her out before you go out. But I do think obedience classes will be a great boon for both her listening during distractions and being around other dogs. It would be very helpful if you can find a few buddies that will go walk with you ... keeping the dogs on leash, separated, but just strolling around getting used to being around but not playing with another dog.
You may get a lot more out of it if you have obedience well underway first, so that you are fine tuning her there. Mary's site has just about every basic training, and she is simple and easy to understand.
Okay so on your dog mix... If you can afford it, I'd do a wisdom panel. It isn't cheap, but it is excellent. I hope for your sanity they find your dog is NOT actually a Carolina dog because ouch. Both basenjis and carolina dogs are "primitives"... and although Basenji DNA is more consistent than the Carolina dog (which has a lot of other breeds mixed in since they lived wild in the USA with a lot of other breeds around to mate with, whereas until recent times Basenjis were more isolated from other groups), you've got a double dose of "yeah maybe I'll listen, maybe I won't... and I really am good at running off and doing my own thing." Having the DNA might help show how much of the primitive genes are in there. Sadly the Wisdom Panel doesn't test for Carolina dog as a breed, and I can't find any that do. But they can look for those primitive lines.
That said, having lived in SC and living in GA, I have met a few Carolina dogs. Obviously with my love for Basenjis and Chows, I'm fond of the primitives. But you have to train smart. Really glad you found the forum, will be fun watching her mature!