He should adjust in time to losing his companion. However long that takes is questionable though and he will continue to be angry and feel neglected and reflect that anger with destruction just out of loneliness. It may improve with time and may not. You have to ask yourself is this fair for your dog? I would spend nearly all my time with him when I was home taking walks, etc. and if you can't do more than 2 hrs. it may be best to find a better home for him where he has a better environment. If his new home is a better place where there is a yard to run, and owners that can spend more time with him he will gradually accept the new home and owners. I know that is hard but may be the best. When your living situation improves you may think about owning another dog.
Other than that, working 2 jobs leaves the dog alone too much to be fair so you need to get someone…the same person all the time... over to your apartment to spend time with him if you don't want to give him up. He can bond to that person and that will help the loneliness somewhat. If you decided to give him up, the new owners could come over frequently for walks and visits before you gave the dog to them so that the dog would consider them friends before adoption, that would help the dog transition. I would not give that dog to an inexperienced owner though. That could end in disaster. It will do the same things with the new owner although it should get over the transition quicker because it will be in a better environment. Also, was your husband the dog's leader? You now have to be a positive leader for him because it sounds like he lacks leadership.
Driving/travel Issues
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Basenjis like to see, and not just in the car. When we moved from the farm to a house in town, I was worried about how my boy Perry would adjust to the change. As it turned out, he liked it from the get go, because of the big windows that he could see out of without having to jump on furniture to have a view. As soon as our furniture arrived he settled right in. In the car, I think they are happiest when they can see out.....but some will get sick if they are riding backwards and looking out the back window, as in some hatchbacks if they are behind the rear seat. Found that out the hard way with my Border Collie. Riding shotgun suited him much better!
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@elbrant It goes on till we get where we are going then he knows when we are going home because he is much more relaxed. So we do not go on many car rides.