After reading all of your updates Chassy, I believe your girl friend has tons of potential. Even though she still has a phobia, I don't think it's as bad as it could be. I think there is a good chance she will get over her fear. She might not necessarily be a 'bird person', but maybe she can tolerate them and enjoy watching them from a distance.
I would take things slow and show her the good and calm qualities of the parrots. Once she seems content enough, I would take steps closer and show her a parrot sanctuary and the loud and 'fluttery' qualities of the bird. Slowly but surely.( I know you brought her to a sanctuary so that's a step closer).
I personally wouldn't recommend a budgie or finches, canaries, ext, as their very small, active, and fluttery, especially if she would interact with them. Green cheek conures are nice birds. And really small. I loooove Indian Ringnecks because they have such a cute voice and their pretty. But they are one-person birds, and they are rather nippy and grouchy. Very much so. On top of that, they go through a 'bluffing faze' during their adolescent months, and that can put a damper on their owner's mood for a while. Their slightly bigger than a Cockatiel. I would reccomend them to many people, but not to someone who has a bird phobia. (Although actually if she would only want to just sit and listen to his cute voice, having one might work).
I would reccomend a Conure of some sorts, although some of them can have very loud voices. Some species are one-person birds, too. But I don't really think 'one-person birds' are your worry, unless the parrot would love your girlfriend more than you, and she hates him/her.