Biting is most likely the biggest "problem" for people and their companion parrots, yet it might also be very misunderstood sometimes. We must first understand the fact that our parrots are parrots and they are not cats for example. Parrots love to use their beaks, they can do some awesome things with them, open very hard nuts, find the tiniest crack in a nut shell and work on it till it opens, climb all over using their beak, hang upside down on them and also preen their feathers or feed very tiny and fragile babies.
If you take time and observe parrots in the wild and pay attention to how they interact you might notice that they do what your bird is doing to you, they just play and chase each other, simply put up a fuss and yet they are still best friends. On my little video you can see our 2 macaws playing, someone might think OMG, they will hurt them selves, no no, they are very good friends and they know exactly what they are doing, they are playing and at the same time they are evaluating each other to see who is where in the pecking order (this is also important between you and your bird). Most parrots if given the chance will do this, it is natural and it is fun for them, much better than sitting beside each other and looking at the wall...
So now the question is, will we learn to play with our birds or will we try to make them stop "biting" us? See, if any of the two birds in the video wanted to hurt each other it would be done very fast and if they wanted to hurt me, I would have no fingers, yet I still have all ten. So if you ask me how I have done what you can see here then my answer is "I learned to play with them". Yes, I personally believe that trying to stop a Macaw parrot from using it's beak is unrealistic and probably very much not fun for the bird and after all even for me, I like to play rough with them, I want more than have my best pal sitting on my hand, just as much as they do and when the mood is for cuddling then I cuddle them, but I truly never expect to have a large parrot who doesn't want to play with me using their beak. I think I can say that I have accomplished the highest level of tameness with my birds as you can see in my Training - Tame Parrot video.
I also have a tameness scale on my website, it has been written by someone else, but I quite like it and agree with it, maybe you can evaluate your birdie by it if you like and set a goal for your self.