Where I am this guy would be adopted in a heartbeat but Texas is a whole different ballgame. Kudos for your work.
Ditto for where I am. I move a lot of dogs out of Texas, I don't think I've moved any dog TO Texas. (no, that's not true, I just moved one OK to TX... same difference).
Please post his picture so we can see what he looks like. Basenji Rescue And Transport https://www.basenjirescue.org/ can help find a good home for him if he is indeed purebred because, like you said, they are not like other dogs. And if he has been on the streets for awhile, he may need a bit of rehabilitation before he goes to a new home.
That's actually a bit of a presumptuous statement, you don't know anything about her level of experience. There was a time that I didn't know that much about Basenjis, I learned, we are now on our 6th and 7th. Yes, they can be a difficult breed, but that in itself is not necessarily a reason to tell someone not to get one.