My friend's dog at work has this problem. He is not a basenji. He does however have an allergy to soy, palms, poutlry, oak pollen and a handful of other things. the spaces between his toes would get beet red or have dried blood in them.
you could try some benedryl. I buy the childrens chewables and dose it out by weight.
or you could test the diet and try one of those foods that is hyper sensitive.
when Beta was diagnosed with Irritable Bowel Disease, the vets cut out wheat, rice, and corn. They said to find a diet that would mimick foods that were found in the basenji's native landscape.
i believe there is an allergy panel that a vet can do, but it is really expensive.
you could test it by feeding your basenji boiled chicken only and see if there is improvement. that may be a cheap way to test a food allergy theory.