I don't think anyone ever suggested Jefferson was an atheist. Nor is there any evidence that Jefferson was skeptic or agnostic about the existence of God. The debate seems to involve whether he was an orthodox Anglican Christian, a Unitarian or a deist.
The impression I get is that Orthodox behavior and language most like were survivals of his upbringing and not a reflection of the views of his maturity and old age. So what we're left with is the question of whether there is a difference between Unitarianism and deism. The definition of words like "Savior" and "salvation" and "our religion" is also relevant.
My guess is that there was a split between Jefferson sitting in his Anglican church or in his office at the White House, and Jefferson in his library or in his correspondence with close friends. Jefferson's "natural piety" and sense of responsibility were inspired by his office and this led him to be more disposed towards Orthodox theology, while his reading and writing reflected very different views. The chief executive of a great nation has to grant some validity or standing to the beliefs of his constituents, and great responsibilities awaken a belief in Providence. Other Presidents, most memorably Lincoln, are indications of this.
As for the often asked question of what Jefferson would do now it's difficult or impossible to answer. His background influenced so much of what he was and did, and that background is gone. Any eighteenth century officeholder would invoke God's name in important documents. What someone of Jefferson's ideas and temperament would do in our environment, really can't be determined. First of all, it depends on the answers we want to get: a Jefferson who accepted slavery, advocated frequent revolutions and the guillotine, and opposed standing armies might not be to our liking. Secondly he changed his mind over time, and his theory and practice differed. Also, you have to choose one side of this many-sided man and say "This is the essential, this is what he would carry forward to our own day," and answers about this will differ.
A case in point, is your stating the question as to Jefferson's religion as to whether he was an Orthodox Christian, a Unitarian or a deist. The structure you have set up is fallacious. He was an individual, who as most of us, strove to appreciate the truth. To even attempt to neatly classify him in terms of a broader array of theological types is to fail to understand that the actual Jefferson was none of the above. He believed that the God identified in the Bible was the Creator. He believed some of the teachings about that God and he doubted others--particulary as they had been translated and recorded. What he believed and what he doubted was set forth in a great wealth of writings. Why do we need to have a precise label for the end result? What clarity does the label add, that may not be found in his writings?
Take another example, of what you say. Jefferson did not "accept slavery". He believed it was a major mistake and involved a major injustice. He did not have a clear idea on what could be done about it. He was aware of the chaos that simply freeing the slaves, without a clear program for what would follow, could bring. If the past century has not confirmed Jefferson's skepticism on that issue, I do not know what would.
It is a serious mistake to judge the Founding Fathers as men who reflected merely their own era. They saw the problems of their era from the persepctive of the entire human experience. It is indeed that ageless quality that distinguishes them from the nearly incompetent political leadership of our day. They thought issues through from the standpoint of human history--not from how they would sound in thirty second sound bites.
William Flax Return Of The Gods Web Site