This is really out of my League.
(1) But, seems to me that he would have drawn the whole story rather than just pages 2 and 6.
My feeling was that the gag was that the bird swore or sang rude songs. The 'Prof' is royally annoyed and hasn't tied the bird up so securely just because he had 'lost his voice.'
(2) Didn't Barks do a similar gag at some stage? He used Parrots more than once. The pages explaining what the bird sang are missing, which is possibly because the story was vetoed by the editor or publisher who never gave him the vetoed pages back.
Who knows? Great find anyway, Robb!
(1)The entire 6-page story WAS drawn and fully inked. We just don't have access to the other pages. Whoever bought them in Clinton's estate sale hasn't shared those pages publicly. Yes, perhaps the bird sang rude songs, so the angry Professor Foxy couldn't dare share his wonderful discovery with the entire nation in his advertised live radio broadcast. My adding in Page 4, show that you may well be correct. The Parrot has a rebellious attitude, and likely used language The Professor didn't like, which could embarrass him in front of The American public, so, in the professor's attempt to shut the bird's beak, the latter bit him on his nose. Thus the strapping of the parrot to the wall plaque.
I doubt that the story was vetoed by his editor, his partner, Joe Barbera was the editor. The publisher (3rd partner (Controlling partner)) would not have rejected a story. Both Eisenberg and Barbera were well-versed on the dos and don'ts of small children's cartoons and comic books. Eisenberg had been drawing lots of "Tom & Jerry" comics for MGM (Dell Comics/Western Publishing) for quite a few years. I think it's a lot more likely that the story never got published because their controlling partner cancelled the series because of a dirth of sales.
(2) Yes, Barks drew Scrooge's pet parrot saying very rude words to someone who Scrooge needed to have a good impression of Scrooge.