What you describe is not a breeder by any standard.
“when we put a collar on she was attacked and dragged around the pen by the entire litter.” The litter evidently trying to sort it out, often dogs will do so without human involvement. They understood the runt was unstable and acted accordingly.
“She then snaps randomly with vicious biting.” Very unlikely, she snaps for a reason, there will be warning signs although you may not see or understand them. Watch her ears, her eyes, her body posture.
“Not our first puppy.” Basenjis are not your average dog, do you mean not your first Basenji? I was vastly experienced with other dogs before my first Basenji, it did very little to prepare me.
“The Dam is the expert trainer for proper behavior. We do not know how to replace or replicate that training.” You have to be the leader, earn the trust and respect of the dog and maintain the leadership position. She sounds like a fearful aggressive dog, they are not easy to deal with but it can be done. Long structured walks help but I do mean long, five miles a day at least. A good trainer will also help, the expense means nothing, preferably with experience training basenjis.
There are very few dogs who can not be helped and trained, however it is a long and labor intensive process.