Another possibility might be Rat Terrier. They do come in brindle, although that colour is out of favour. There is one in my neighbourhood that has a bit of a Basenji look to him, and his tail is very short.......not sure if it's natural or docked.
Can see all the pics now. What a good idea to let the younger Basenji spend time getting used to your cats. Trouble is if it were me i dont think i'd want to give her back 😃
