We were living in Salt Lake when we first decided to get a basenji, and while there is at least one sketchy backyard breeder in Ogden, I was glad we went elsewhere. We'd moved to Seattle by the time we actually got a dog (brought home Jan 2017), and so got one there locally from MaryK Quinnett, who isn't actively growing her program right now.
While doing research on the breed, we went to a lure coursing competition and talked to Kevin and Theresa (I think? people names seem to take a back seat to dogs' names) of FoPaws Basenjis, who are located just outside of Portland. http://fopawsbasenjipuppies.com/ We went with a closer breeder, but I wouldn't have hesitated to get any dog they'd have chosen for us, and it's a reasonable drive from (at least northern) Utah. There are several more in that area, I think. Plus a bunch more in Washington State. And in California.
The other thing I might recommend is to take a look everything from the Evergreen Basenji Club (www.evergreenbasenjiclub.org). They seem to be a bit more active than a lot of other clubs and tend to include just about everyone in the northern half of the western United States.
We have since moved to Texas and added a second puppy to our pack this April, and it was kind of a pain to wait after we'd decided--there was really only one legit breeder with litters in Texas this past year--but in the end it was so very worth it. I grew up with cats, so our 11/16 basenji female and 1/18 basenji male were my very first dogs, and I can't imagine how much more difficult things would have been with poor temperament breeding. Basenjis are amazing, but it seems like there just isn't much room for error when it comes to temperament and personality.
Have you met any basenjis? When visiting family in Utah with our dog I was told over and over again that the person speaking had never seen a basenji in real life (including at pet shops and doggy daycare), so I get the impression that the odds of tracking one down locally to meet might be difficult. I wish I were going to be bringing my dogs there soon so you could meet them, but maybe you've already had plenty of experience with the breed? The things I've posted on my Instagram (@zannahdo) is a pretty accurate representation of what life can be like with a basenji, if that's in any way helpful. Feel free to ask us more questions; this is not a breed for an impulse purchase (and, as you've found, supply makes that fairly impossible anyway).