The date

I was going over my notes and sources again today, when it suddenly hit me that if they rested from dusk to moonrise that first night before going on, I should be able to figure out the exact date. My 200-year calendar doesn't go back far enough, so I searched online and pulled up a calendar for 1757. There were four Sundays: 4, 11, 18, and 25. When I checked the moon's phases, it was obvious that the only possible date was the 18th--September 18, 1757.