I don't see "over" giving the statement any deeper understanding. Over, to me, confuses what Jesus said.
The word you put forth, anōthen, is found 13 times in the Bible. Here is how the NT writers used that word.
- Matthew 27:51 = "And, behold, the veil of the temple was rent in twain from the top to the bottom; and the earth did quake, and the rocks rent..."
- Mar 15:38 = "And the veil of the temple was rent in twain from the top to the bottom.
- Luke 1:3 = "It seemed good to me also, having had perfect understanding of all things from the very first to write unto thee in order, most excellent Theophilus…"
- John 3:3 = "Jesus answered and said unto him, Verily, verily, I say unto thee, Except a man be born again, he cannot see the kingdom of God."
- John 3:7 = "Marvel not that I said unto thee, Ye must be born again."
- John 3:31 = "He that cometh from above is above all: he that is of the earth is earthly, and speaketh of the earth: he that cometh from heaven is above all."
- John 19:11 = "Jesus answered, Thou couldest have no power at all against me, except it were given thee from above: therefore he that delivered me unto thee hath the greater sin."
- John 19:23 = "Then the soldiers, when they had crucified Jesus, took his garments, and made four parts, to every soldier a part; and also his coat: now the coat was without seam, woven from the top throughout."
- Acts 26:5 = "Which knew me from the beginning, if they would testify, that after the most straitest sect of our religion I lived a Pharisee."
- Galatians 4:9 = "But now, after that ye have known God, or rather are known of God, how turn ye again to the weak and beggarly elements, whereunto ye desire again to be in bondage?"
- James 1:17 = "Every good gift and every perfect gift is from above, and cometh down from the Father of lights, with whom is no variableness, neither shadow of turning."
- James 3:15 = "This wisdom descendeth not from above, but is earthly, sensual, devilish."
- James 3:17 = "But the wisdom that is from above is first pure, then peaceable, gentle, and easy to be intreated, full of mercy and good fruits, without partiality, and without hypocrisy.
So Matthew, Mark, Luke, John, Paul, and James all used the word "aonthen" in this manner.
It doesn't seem to mean "over" as in "re-do". It seems to mean coming from above, or being first or from the beginning or top as in preeminence.
To be born "again" is to have a spiritual birth that takes priority over the fleshly birth. Born "over" just mean a re-do.
Born "anothen" mean a different birth that takes priority.
