For our family, we HAVE to crate the dogs when we leave. It's for their protection and for our home's. I would never ever take the risk of leaving them out and possibly coming home to destroyed stuff. No thanks. We did it ONCE and we lost the couch. I wish we could….
Get her a cozy bed to sleep on either in the closet or next to your bed. Work diligently on training her to sleep in her bed at night. Chances are, she'll eventually take to her bed over being crated.
Basenji's are social animals. My little Lexi LOVES other dogs. All kinds. Well, she prefers big dogs, but it's not unusual for B's to like other dogs.
And yes, eventually they calm down SOME... My little girl didn't calm down until 3 or 4. We just rescued Miles and we don't know his age. But he's a wild one!! I think they will always "activate" and do the B-500 every once in a while. That hasn't changed and Lexi's almost 6 now.
Stick to your guns. It will work out. You could always get her a pal...