Must have been a horrific stench! Many unpleasant odors combined to make one big stink. Imagine the intensity in Gettysburg when the aroma was noticeable in New Jersey. In this area it is typical to have weather originate and winds/breezes prevail from the west, thereby carrying airborne particulates like aromas to the east. That's still a long way for a smell to travel. Here is a quote from accuweather:
Ben Neely, Executive Director at the Adams County Historical Society, emphasized that the most damaging aspect of the weather for this event actually occurred on July 4, the day after the battle had ended. Rain fell across the area for most of the day; Rev. Dr. Jacobs put the total at 1.39 inches. While wounded still lay on the field, some may have felt welcomed by the break in action. Some wounded soldiers had still not been moved from low-lying areas by the Plum Run Creek, however, which overflowed its banks. Those stranded near the flood waters, reportedly all Confederates, drowned.
Not sure if this heavy rain would have diluted the odors or helped whisk them away to be sniffed by others.