We're working to implement some of the ideas like the toy basket and stuff and its beginning to work already. I think a big part of the problem as far as chewing on things they shouldn't when they're out with us is just that they've gotten tire of the toys we had for them. We made some new ones and they seem to be more interested in them than anything else right now.
One note about our grey: she has no toes. She has a play stand, and she perches on it sometimes, but she can't really play with toys while she's on it. We tried a flat perch, but she doesn't like it very much. For some reason she prefers the rounded ones even though she can't grab them. We've got a hoola hoop gym under construction, and we're going to hang toys from the ropes that hold it up and attach them to the hoop in the hopes that she'll be able to perch and play at the same time, but she doesn't seem to like hanging toys (maybe because she can't stop them from swinging). Because of this, she mostly plays on the ground.
We're back on the fresh food train. It turns out smoothies are the answer to all of our woes in that regard. The birds don't want to EAT chop, and chop is harder to make. Smoothies are easy, and the birds love them so its a win win. We cut way back on fruit. We put just a little pineapple in their green smoothies (so that they'll eat it), and we give Picasso blueberries when she goes to the Whole Foods with us.
As to the beaking, I've read conflicting reports on this, and I'll have to consider it for a while. Some resources say, "if you let them beak, they'll bite." However other research indicates no strong correlation between beaking and aggressive biting and I have to say we've found the same. Sure, sometimes they get too rough during play, but we let them know and they back off... when they're playing. The issue we really want to deal with is biting to get their way, or for aggression and if I can do that without eliminating beak play I'd like to. So, if anyone has some resources available from that perspective so I can give it a try, I'd be grateful.
I recently read that being trained is actually a rewarding experience for the parrot too...some mental exercise and bonding. Is the clicker the same as you'd use for a dog or is there a special one for birds?
Recently my bratty macaw decided she will only eat her greens if I sprinkle some diced almond on top... which is fine with me as she does need good oil in her diet. 
At first I was worried about the mess of the dropping my macaw would make. Luckily by giving her the right foods, her droppings are solid most of the time unless I give her stuffs that are watery like cucumber and watermelon. So picking up her droppings aren't that hard or disgustful. After some times of observation, I do able to get her to her stand to do her business but the brat would refuse to go on her stand. She also knows where you should potty which is her stand but again...if I did something naughty (that I didn't even know my self), she will poop on the floor to get back to me. Yup she is vindictive. 
