lordofspeech, you have a lot of interesting things to say. I agree with what you're saying that Benanti shows gumption from the get-go. When she shows up at Higgins's house for speech lessons, she seems to arrive with the idea of selling him on the subject. Ambrose seemed much more tentative, much more "I know I don't belong here and I'm asking for something I might not get."
Benanti also doesn't seem to care that her father has no fatherly instinct towards her. She's not very emotional towards him in any direction (hurt, anger, resentment, etc). Presumably, her Eliza made peace with the situation a long time ago. I don't get the idea that she and her father were ever close.
I found with both Ambrose's Eliza and Cynthia Erivo's Celie, the story was about their journey to discovering the strength and character within them that they didn't know they had. It was a revealing to themselves as opposed to a new strength that they developed over the course of the story. With other actresses playing Celie, I felt more that they developed their strength over time. Benanti's Eliza is strong all the way through.