Melvin is gorgeous!! I love him I agree that the person's tone was rude in their letter. I would have been offended by it. Chickens are beautiful, clean creatures and are more hygienic than dogs, and indeed most people too!
Apart from an egg song or a predator squawk, my girls are quiet all the time! I have brown hybrid layers. If it's a very noisy 'bawk bawk bawk bawk bu-CLUCK bawk bawk bawk' type of noise they may be feeling threatened by your cat. My chickens chase cats lol! And they make no secret of the fact...
Keep trying the vet, and tell them it's life and death - it really needs to be the correct antibiotics and they will likely provide her with some pain relief too.
Ah ok if you were in WA I would have directed you to a good avian vet but you have one already, so no need! Please let us know how Onslow is after her vet visit, she is a very well loved hen