I think you've summed things up pretty neatly. I would just point out one thing, namely, that I (nor I dare say, any other "fundamentalist") would not disagree that God kicked Adam and Eve out of the Garden in part to keep them from the Tree of Life.
Genesis 4:23-24 - So the Lord God banished him from the Garden of Eden to work the ground from which he had been taken. After he drove the man out, he placed on the east side of the Garden of Eden cherubin and a flaming sword flashing back and forth to guard the way to the tree of life.
So these verses explain that two reasons God kicked Adam out of the Garden were: to work the ground and to prevent access to the tree of life.
However, to claim this as the only, or the main purpose behind Adam's exulsion from the Garden is to deny the plain reading of the prior text which you posted.