1. From the Rennaissance up to the beginning of the twentieth century, history records the steady advancement of the rational mind
Steady advancement? Where? And exactly what do you mean by "the rational mind"?
2. But the twentieth century also revealed the formidable fortresses unassailable by rationality and impervious to logic.
Do you seriously believe that?
3. But, in my mind, the Dark Lord of Logic was always Kurt Gödel who found the Achilles heel of rational thought.
Nice idea - but I think Gödel himself would be offended at being called a "Dark Lord" and he certainly would not see his Incompleteness Theorem as an Achilles heel of rational thought. He did not see a consequence of his theory that "irrationality" was about to parade down Main Street.
4. Just like the dogmas of religion, the days of rationalism are numbered. The writing is on the wall, written by the mathematicians and physicists who wielded its power. It is always the wizards, the alchemists, who first understand that the jig is up.
What do you mean by rationalism? Who were/are its proponents? How does anything Godel say contradict rationalism as you so understand the term?