Try switching to chicken or turkey based foods.
Here's a link to an excellent evaluation of kibble brands:
I would also be careful what you put on your hands before cuddling with your dog; lotions, essential oils, etc. can cause allergies in dogs
And Best in Show was a whippet "Bourbon" - it doesn't happen very often that a hound breed wins BIS
Ditto to everything said by others. But also keep in mind, just because an owner says her dog is not in heat doens't mean her dog is not coming into heat. My Teddy can tell a bitch coming into heat a day or two before the human knows it. If there are intact dogs at your dog park, stop going there (I don't recommend dog parks either).
As mentioned basenjis require positive training techniques, consistent consistency, mean exactly what you say (is "down" for get off or is "down" for lie down?), have patience, training needs to be fun (always use happy voice never yell or reprimand), PLAY with your basenji at each training session (read When Pigs FLy as suggested).
When you take a obedience class, never worry about the other dogs and how fast or slow your dog responds relative to them (this will require you research possible intructors). When my male was in class and we were learning the down command (for lie down), other dogs would have it in one or two sessions BUT my instructor understood basenjis and said No Worry, he'll get it - it took almost 9 months but he finally did it (patience needed).
My dogs have Rally Master titles, Master Agility title, Intermediate Tricks titles, and Barnhunt title. It can be done.
I took my male to one when he was about 2. First went in the small dog area (where there was only one other dog) but the grass was so high I was afraid of ticks. Then went to big dog area and mine just wanted to sniff the fence area until some bullies came along and started to really pester him - he took off for the far corner (thank goodness). Forget the dog park.
Sorry it took so long - the vet checked her out and she pinched a nerve (apparantly when she tried jumping on the bed). He checked for tick diseases, organ functions, etc etc. All fine but the x-rays did show a bone spur on one of the lower vertebra so that little jump was all it took. She's walking much better now and almost back to normal.