Well…there will be no breeder here willing to 'help out'. No responsible breeder will stud their dog out to a possible basenji mix bitch, because someone wants puppies just like her....
are you by any chance, a troll? This sounds like a text book troll post to get everyone all fired up
If you aren't a troll, I apologize, and would direct you to the many threads here about why breeding is a huge responsibility, it is something you do to preserve and/or improve a breed, not because you love your dog, and you want to see ones just like her; or because your kids want to see the miracle of birth; This in no way impunes your integrity as some one committed to rescue...but honestly most rescue people will shudder to read your post.
Refusing to stud to your bitch has nothing to do with outwaivers, or liability, or reputation...it has to do with not protecting the breed. Caretakers of the breed just don't do that