Hi Mark – It's me again, Sharon & Nala...I think I'm reliving Nala's puppyhood through you and Cali! Nala would poop in her crate as a pup too. I know I tried making the crate smaller with a barrier, but she still pooped. I think I tried just about everything that was suggested but suffice to say, she doesn't poop in her crate (unless she's ill) now. If you haven't already, I would go out and buy a HUGE container of the doggie enzymatic cleaner that neutralized odors...hang in there...patience, my friend, patience...
A few more suggestions to might try . . . aside from realizing you have a little bitty Basenji, patience is due as her cleaner instincts will kick in during the house training phase. My suggestion is to put in a teething toy or two in her crate and a t-shirt you've worn with your scent for comfort and security. And you might try putting a bowl of kibble in too. It is against doggie instinct for them to eliminate where they sleep and eat. It might just do the trick, whether she eats the food or not. I don't think a full helping of kibble in the bowl is necessary, just enough to indicate food is present. I would use stainless steel bowl in case it becomes the object of chewing attention.
I remember coming home to a poopy crate too last March & April when we got Duke. The $18 soft wonderful crate bed was thrown in the garbage. I got tired of washing it every night. I was advised by a trainer that puppies don't need that and to let him lay on the bare crate tray. It was much easier to clean too. I used Nature's Miracle to clean the smells from the crate. Very important to get rid of urine and poop odor. I think the crate was poop free soon after getting rid of the cushion.
My sympathies during this young-puppy phase. It will be worth it - Good luck and enjoy your forever little one.