I think you described it well. There was one biblical figure left out of your list that is significant to Islam. They put that person, a son after the manner of flesh, a literal bastard, in the place of the son after the manner of promise.
I'll put a link here to Genesis 22 though I'm confident that you know that story.
For centuries, the Muslims have contended the scripture was changed. It's a nonsensical claim, for there are more than enough existing copies of Genesis which pre-exist Muhammed by centuries.