...here is my question: is intelligent design completely incompatible with evolution? Is it not possible that there is a supreme intelligence behind the whole process of evolution?
I realize my Judeo-Christian roots are very evident, but I am asking the question in all sincerity. Are these ideas completely incompatible?
Yes, I would say intelligent design is incompatible with evolution. Remember that "intelligent design" is a specific theory that argues that because we can't find the connections between some odd disjunctions in evolution, it proves that existence must be the work of a designer. Evolution sees life on Earth as a continuum, one species arising from the changes in another over a period of millions of years. Intelligent design argues that a designer created some species spontaneously.
Your second question is different from your first: is it possible that the process of evolution is one of God's creations? This is similar to Deism, the Age of Enlightenment philosophy that stated that God created the universe, gave it laws by which to run, and now leaves His creation alone and doesn't interact with it. However, clues to God's existence can be found by studying the natural world, all of which brings us back to Darwin on the Galapagos Islands.
Darwin's wife was a believing Christian, and reportedly concerned that her husband's work would destroy religious faith. Darwin, in turn, was very sensitive to his wife's beliefs and discussed his theories with her extensively before publishing. Their's was literally a marriage of religion and science.
Since the publication of The Origin of the Species, people have had to reconcile their religious beliefs with Darwin's theories. Don't forget there was a scene in the NOVA special which showed two of the teachers who brought the suit against the school board with their church group. They talked about how offended they were to be called atheists simply because they believed in science.
Pierre Teilhard de Chardin would also have been offended. He was a Jesuit priest who was also a paleontologist and he sought to reconcile the two. He believed that evolution has a goal (a design, if you will), which is for humans to use their ability to think as a way to grow spiritually and move towards higher consciousness, ultimately towards God. de Chardin did not see religious faith and evolution as incompatible, but as intertwined processes taking us to the same end.