For pellets I would suggest either Harrison's or Totally Organic Pellets. Try buying the small bags at first. I know it is possible to get samples of Harrison's pellets because I've seen them in stores but I'm not sure about Totally Organic Pellets. A small bag of Totally Organic Pellets is something like $5 though so it is easy to buy one to try out.
I think it would be best to offer both brands and rotate them but it is not necessary. I found three of my birds like both brands and the other two prefer one brand but will eat the other as well. Harrison's makes a variety of different pellets and the kinds my birds like are Harrison's Lifetime Fine (these may be too small for Reggie) and Harrison's Pepper Coarse. Reggie would probably like the Pepper ones.
What are the other problems? Punishing? Doesn't work too well. Birds are different from dogs and humans. Well, it has to be done differently. My idea of "punishment" is to put the birds back in the cage. If they are being very bad and not listening then they go right back in. This only happens with Malachite! The others are so well=behaved but he can be a little monster. I try to give him options though. First I tell him to stop doing whatever he is doing that drives me nuts, then he ignores me and keeps doing it, then I tell him if he doesn't stop he's going right back in the cage, then he pauses and looks at me to see if I am serious, and then he usually stops.
That's about it though, I don't really think it makes sense to be negative to birds when they are doing bird things like ripping everything apart and pooping all over the place. That's what they are naturally inclined to do. If I don't want them to rip something up I don't put it in any of "their" areas. They don't intrude into my space, except Iggy. She has an obsession with books and she knows she is not suppose to chew on them so she sometimes secretly hides and tries to chew silently.
What is she doing that is driving you nuts? If it is biting I may not be a huge help. My birds have never really bitten me. Iggy bites gently for fun but never breaks skin or really hurts you. Squeaky once tried to eat my hand accidentally while eating some pellets off of it but it didn't hurt too much. The one time I was bitten by Malachite hurt quite a bit. He was just learning to fly and had overestimated his abilities (men!) and was going to fall to the floor so I put my hand underneath him to stop him and he hung on. To my finger. With his beak. He was scared because he was falling so it hurt. Didn't break the skin though and it was definitely not on purpose. Romeo and Juliet have never bitten me. They've bitten my boyfriend though, especially Romeo. Romeo once latched onto the finger of his leather glove and refused to let go. He was just dangling there like a pit on a tire hung over a tree limb.
I do not care to be bitten at all. I'd rather take on an angry dog than an angry Amazon. I was bitten by an Amazon and that one really, really hurt. My hand was numb for a while after. I don't ever want to experience that again. If she is biting you should probably use a stick to move her around instead of your hand. Here is a post a birdie friend made about these cool things you can buy to help you move a biting parrot around safely.
http://www.emmalogue.com/2011/04/hand-saver-perch-from-exotic-wood.htmlHopefully you will be able to figure everything out with Reggie. It's sometimes difficult to understand what motivates parrots. Other than food of course. But, to be honest, I'd probably prove to be very food motivated!