We are still praying and sending basenji hugs your way… BTW did you ever get the blood work done? I know your Vet. didn't seem too interested in doing blood work... but maybe there is another clue as to what is afflicting poor Booger there. Maybe you could get a second opinion from another Vet.? I know how hard this is for you, we do wish the best for you.
I will be thinking of you and hope you are able to get to the bottom of this. His health has so declined that SOMETHING is being missed. I assume they have checked for autoimmune hemolytic anemia? I'm not talking about the inherited kind, but the idopathic type. It is easily found if they do a PCV. Lethargy is very consistent with hypothyroid but not the weight loss. It would be the opposite – he would gain weight without eating much. Please let us know. This is very sad.
Any chance you would be open to taking Booger to a totally new vet/clinic. A fresh pair of eyes to look at the situation. Ask for his records and just get a second opinion. To use a lame quote – sometimes one can't see the forest for the trees and I'm wondering if this isn't the case here.