Some things cannot be fixed. I urge you to get a qualified behaviorist (veterinary) to evaluate him. If he is truly unstable, rehoming him is not fair to him or the new home.
Yeah, I'm kinda interested in knowing what this means, just curious:
"Unfortunatly I am at a point in my life where I can't provide him with the proper care that he deserves."
We have an basenji rescue who works through out the whole US.
So, if you would like to know about listing your basenji with BRAT please go to http://www.basenjirescue.org
We would be happy to help you rehome your dog to a very good home.