Yes, I have 3 x rehome and rescue Amazons.
Ollie Orange-Wing was the first. Very scared of humans - even eye contact would send him scurrying to the back of the cage. Never thought I could ever touch him which was fine with me. He was cage bound for the first 1.5 years so after I worked on approaching him, I then worked with him inside the cage. It took 6 months to be able to touch his head and gently give him a scritch. He still has a phobia about hands which is fine. He will now step up on a hand held perch, he can touch a target, he turns circles on cue, he'll hold his feet steady so I can cut his claws. I also taught him to enter a travel cage for our house/country move (it took year to teach him!). He has climbed down on me about 2 or 3 times and stepped on my arm which I was amazed at. I love Ollie so much - he has gone from being incredibly fearful to swinging upside down on hanging gyms etc. He's a real clown now and enjoys life enormously despite having Aspergillosis (methinks from being stuck inside a tiny, incredibly filthy cage for 4 years). Ollie has been with me for 9 years.
Chico (Panama) is over 50 years old and came to me extremely aggressive towards women. His aggression nearly got him euthanized. It has taken a lot of work to be able to skritch his head through the bars of the cage and then without bars. It was very difficult to interact with him to begin with as he would just climb the bars to lunge and try to bite, despite being wracked with arthritis. He wouldn't take any treats so it was hard to find a reinforcer to work with. So I could only use desensitization until he realized he LOVED skritches. I've had Chico 5 years and it has only been this year that he has begun greeting me like he would a male human - by coyly scratching the side of his face. I feel we have an understanding now. He is just about blind but will come to take a treat from me when I tap the cage bars. To be able to clean out his cage, I get him to station for skritches so that he doesn't chase me. Here he is waiting for a skritch...
Bobbie Red-lored was unsure of me at first. She couldn't fly when she first arrived but over the 5 years she's been with me she has been practicing mostly using the settee as a landing pad. She gets so excited at take off she lets out a squawk. She's pretty good at flying now. She came to trust me pretty quickly and would rather hang out with me than with her birdie friends. I've taught her to target and turn circles on cue.
Would Annie bite if you offered your arm instead of your hand? Or get her to step up on a hand held perch for a treat? You want to try to get her out of the habit asap. So maybe use a perch whilst she's getting to know your arms/hands. Will she take treats from you? That might be a way of associating your hands/arms with something good.
When she does step up on your hand/arm, can you reinforce with a treat? Then put her immediately down again. When she's doing this with no hesitation, then start teaching duration (the amount of time she is on your arm/hand) before giving her the treat and putting her down again. So first time 1 second. Treat and down. Next time 2 seconds, treat and down. Reason for the treat is that she will be physically unable to bite you and reach for/eat the treat at the same time. Reason for putting her down immediately is so that she doesn't even have the opportunity to bite. She'll start to associate stepping up with good consequences. Later you can fade out the treat and use more natural reinforcing consequences like carrying her somewhere of value to her or playing with a favourite toy.