As someone who actually has 'misophonia', courtesy of ADHD, I've just got to chime in to say...
LET YOUR BIRDS OUT WHENEVER YOU WANT.
No one's disorders are their neighbour's problem. I get hot flashes of rage and terror at the sound of doorbells ringing and people knocking on doors, but uh...I haven't demanded that my neighbours upstairs dismantle their doorbell or some nonsense, lol.
Drop some 2¢ earplugs on her doorstep and be done with it. Your house, your yard, your aviary, your birds. Be happy and let her wallow in her miserable existence without letting her drag you down with her!
Perfectly said.