The important question is, what is his quality of life compared to what it would be?
When my ex (Andrew) & I broke up, he got Booger & I got Lola. Lola was 15 months old, and went from living in a 2 dog, 2 owner household where somebody was almost always home, to living in a 600 square foot, 1 owner, no other dogs household. I frequently was gone for 12 hours because of work. She had not been consistently crated until I moved, (nor was she reliably house trained because Andrew was a lazy jerk but I digress)…
Within 2 weeks, she stopped hiding under the bed when I left for work in the morning. She would RUN to her crate, sit & wait for me to treat her & close the door. Within 2 weeks, she was 100% house trained. Was it ideal? No. I would rather spend 24 hours a day with her, but keeping her crated during the day kept her safe. Also, when I take her anywhere with me now (dog shows, lure coursing, friends' houses), I can safely crate her without causing her or myself anxiety.
I tried to take her to the dog park or to a friend's house for a doggie play date 2 or 3 times a week. Not the ideal amount of exercise for a basenji puppy, but I gave her better care than what most people give their pets. On my days off, I made sure to spend extra time with her & getting her exercise.
One thing that really really helped was adding a second basenji to the household. I found that on nights when I was too exhausted to go on a long walk or take them to the park, the 2 basenjis could tire each other out running circles, even in the tiny living room. Also, during the day I crate them together so they at least have one another for company.
I know its an awful feeling leaving them for that long, but could you really find somebody who could care for your dog better than you could? Just the fact that you are even asking this question on a public forum means you care for your little guy a whole heck of a lot.
Keep him, crate him, and try to get him enough exercise. They are very resilient animals, and although you may feel some anxiety & heart break over keeping him crated so much, you will feel better than if you rehome him because then you'll worry about how new owners are treating him.
Although it sounds counterintuitive (if you don't have time for 1, how can you possibly have time for 2!?!?), adding a second one actually makes many things a lot easier, for the above stated reasons. I am so glad I added a 2nd for Lola's sake.