so happy to hear that Nanook is progressing well
He looks like an adorable dog and hopefully he's on the way to recovery now. At least the vet and specialist you have now seem to be on the right track..finally,
Did you decide not to make the complaint to the AVMA? I probably would hesitate too knowing that your specialist works for the same corporation. However I'm sure the specialist knows what the first vet did/didn't do and I probably would mention that you feel like reporting him to her and see what she says. You could say it in an off hand manner as though you were just thinking that you'd like to do it but won't necessarily. Then go by her reaction whether you follow through.
The sample that was supposedly bungled by the lab may have been the fact that the sample the vet sent was inadequate for testing or not sent at all and the fact that you asked about it, resulted in them lying to you which would be very bad
You could safely report that vet without affecting the corporation at all. It's quite possible this vet has other complaints against him and the more complaints the more likelihood something will be done about him by the corporation. I hate to think how many people/pets he has misdiagnosed and then charged them a huge sum of money for nothing.
Good luck to both you and Nanook I really hope he continues to improve