Wouldn't feel bad about the behavior of your basenji. I got mine six years ago and he acts a lot like yours. I kennel trained him and when I have company he goes in the kennel till he settles down. When I let him out I just tell people to be still till he checks them all out then he is fine. A lot of times he acts like he is going to attack me if he doesn't get his way vicious snarls and all, but I have learned it is just that an act . He also acted vicious around other dogs but after introducing them properly he gets along great. We have recently got him a new basenji mixed sister to play with, after the snarls and viciousness he loves her very much. I wouldn't be afraid to rehome your basenji, it at least give someone a chance to see what they can do.
