One quick note: the Enola Gay did not bomb Nagasaki. The airplane that carried out that mission was Bockscar and it is on display at the National Museum of the United States Air Force in Dayton, Ohio. Here is the nose art on the plane (added after the war, photos with the crew show no such art) which depicts four "dummy" drops (or "pumpkin" drops) and a fifth (red) atomic mission. Here the plane is on display with a mockup of "Fat Man", the bomb it delivered. The Enola Gay is on display at the Steven F. Udvar-Hazy Center in Virginia. The pilot for Bockscar was Charles W. Sweeney, and the pilot for the Enola Gay was Paul Tibbets.

I will leave the question for other experts, other than the disposition of the planes.