It may help to remove "dominance" out of your vocabulary when speaking about animals. When it comes to our pets, "dominance" doesn't exist. I feel like the word "dominance" is used as a scapegoat for undesired behaviors. If an animal hasn't been trained otherwise, how would they know to act differently?
"Dominance" and "alpha" aka "boss" type training techniques are used to teach animals what *NOT* to do. This is where learned helplessness and extreme aggressive behaviors come from.
Positive Reinforcement,
Force Free Animal Training,
Applied Behavior Analytics,
Antecedent-Behavior-Consequence Training, all of these are about changing behavior by changing the environment, changing our behavior, redirecting undesired behavior and teaching new behaviors. The more that desired behaviors are rewarded, the more likely a bird is willing to perform that behavior. If this new behavior is incompatible to an undesired behavior, that undesired behavior may eventually just fade away because it doesn't get any rewards.
If every time you walk by the cage, the bird lunges, this reinforces the lunging behavior. This, in turn, can result in a bird that is defensive about their cage. You offer your hand? Bird bites. This then leads to cage aggression.
If you were to change your approach to the cage, such as walking slower and maybe talking softly or at least announcing your presence, or perhaps moving the cage to another location so that you are in plain view prior to passing the cage, this may result in less lunging. Pair this with a high valued treat, bird learns to expect your presence with good things. Over time, the bird may become eager enough to see you that they'll readily accept treats by hand. You approach the situation right, no lunging, no biting, no cage aggression!
Simple! And non-intrusive! Understanding and using these techniques *IS* a different way of thinking. A lot of people *think* they are using positive reinforcement training techniques when in reality, they aren't.
What positive reinforcement training is *NOT*: Shoving your hand against a bird's stomach, forcing the bird to step up, then rewarding the bird for stepping up.
What positive reinforcement training *IS*: Teaching the bird to look towards you and rewarding the behavior. Moving their heads towards you and rewarding the behavior. Taking steps (even if it's one!) towards you and rewarding the behavior. Putting a nail or a toe on your hand and rewarding the behavior. Putting their foot on your hand and rewarding the behavior. Putting both feet on your hand and rewarding the behavior.
What is the difference? The key difference is the bird's willingness. Is the bird eager and willing to step up? Or are they stepping up because they have to? Because they can't get away?
I have no doubt that you can form a relationship with your ekkie by changing your approach and figuring out what makes her tick!

(i.e. desired rewards!)