Below is a conversation from Joanie Doss. If any of you know of her, she is a renowned Amazon trainer. I did get Joanie's permission to post it in it's entireity here. I had posted in the amazonasociety about the cage territorialism I am dealing with and she had the following insights. They were experienced and cumulative of her knowledge. Thus, this seemed like a good place to spread the knowledge.
Mark
This is unedited in it's entirety from Joanie:
I have had my males for a long time. (The youngest bird has been with
me the shortest time....17 years).

One Amazon I can always take out of his cage and pick up anytime with
my hand or arm. Two I can pick up 85% of the time with a bare hand or arm.
Two require a stick to be taken out of their cages at all times.

A lot depends on the individual bird. My Nape Sidney doesn't have a
mean bone in his body but he is very excitable and when an Amazon
is overly excited they will bite. He had a history of biting before I got
him. His biting began at 6 months of age and by two, could deliver a
nasty bite.

Amazons bite for several reasons:
1. They are hormonal
2. They are afraid.
3. They are overly excited.

Since you clicker train, you can get her to accept the stick. I strongly
believe all Amazons should be stick trained as well as hand or arm trained.
Remember to move slowly on getting her to accept the stick. I start with
just putting the stick in the room and gradually move it toward the cage. If
the bird shows any sign of stress, I back it up until the bird ignores the
stick or relaxes. Once you can get the stick to the cage, you can start
on clicking to get her to accept it. Finally you are in the cage. Don't
move the stick with her on it until she confidentially steps onto it.
Your little girl could work out of this. I would use a stick, at least until
the pattern is broken. Amazons are not greys with green feathers. They
have a lot of fire and flash. Many rules and statements that are true
with other species of parrots are not necessarily true about Amazons.

We that own and love these birds accept them for what they are and
learn to work around some of their less desirable traits in order to
enjoy their many wonderful ones.
If it means taking them out of a cage with a stick, so be it. Once
out, they generally are pretty mild.

Although I do not know Joanie Doss or have an Amazon, this is sounds like good information for you working with Cleo. Thanks for sharing her insights for others here as well.