It has been several months since I read the base government document that I believe that you are referring too. The National Avian Vet Association has been working hard to lift that travel ban (with in the US) to allow Breeders to move a fairly wide cross-section of New World Parrots to travel across State lines for breeding. I do not recall, which MAC's where on that list, but I do recall it to be fairly inclusive, i.e. most all.
Traveling across State lines with your "pet" is generally allow with in the continental US. Had or if the Avain Flu returned last Fall (which it did not) or again this Spring, a travel ban could be quickly set in place for All BIRDS.
If you are traveling with more than a single parrot of a specific species (example: two DYH Amazons), you should be ready to prove that they are your pets and not breeding stock. The likelihood of you being stopped is fairly low, unless you look like you are transporting a mini Zoo.
It is wise to have recent medical records as to the health status of each parrot that is traveling with you. Not only for clarification of ownership, but should one of your parrots become ill during your travels. Stuff Happens! And, the further from home, the greater the likelihood.