June 5-6 was chosen for the full moon and the tides, with the 5th being cancelled due to weather. What if, for some reason, the speed of frontal passage is underestimated enough that the 6th is cancelled early, forcing a month's wait for the next full moon.
However I forget what the weather was like during the next full moon. Say the weather that night was bad too. (Does anybody have meteorological data links for July 5-6, 1944?)
What if July 5-6 had bad weather too, and THAT scrubs Overlord? Bagraton in the east would lead to a Brown Alert moment for the Western Allies, and they decide, "We can't wait anymore, we're taking the next tidal opportunity," and go for the following new moon...on July 20th.
Overlord goes in on the same day of the Bomb Plot IOTL. Does the bombing still happen, could there be enough butterflies to change it, basically, what would happen if the assassination attempt goes down on the same day as the invasion?