I have come on the forum after a couple of day's absence and have tried to pick out your salient points beyond the disagreements. I'm pretty much convinced that this is a crate issue and I think it's better to concentrate on relieving that problem - there is quite a bit of professional advice on crate training on the net and also as given by some of the previous posts and I would advise you use the links suggested previously for a start. Many of us do have Basenjis with crate problems. I have one particular bitch who just will not accept being crated. After trying all sorts of ways to persuade her I gave up. But i'm lucky in that normally I don't have to crate any of my Basenjis for any period of time and definitely wouldn't have them if I did.
Circumstances obviously dictate that you have to crate your dog but I'm sure you try to make up for that when you're home.
I agree that you might find it easier to teach her to be better behaved when she's left loose in a room for the time you have to be away rather than work to get her happy in the crate (perhaps a combination of both?).
I see that much practical advice has been given in these postings - it's up to you to sort this out but please try to accept that many have extremely strong views and I'm sure don't mean to be unkind.
Personally I don't like confining dogs for long periods at a time and wouldn't sell a puppy to someone that had to, but I do appreciate that not everyone is the same. It's untrue that Uk people do not crate their dogs for long periods as I believe that somebody posted - some do and some don't and I imagine that's the same in any country. People are peoplefter all!
As to the peeing - make sure that you use a product to completely neutralise the smell, Basenjis have very keen noses and washing is not usually enough. She may be peeing because the odour is still lingering.