Going back to the citation about Washington's arrival in New York, I found this report: James Riker, "'Evacuation day,' 1783, Its Many Stirring Events: With Recollections of Czpt. John Van Arsdale (printed for the author, 1883), 14 - 18.

"The city's excitement turned to anger when they saw the Union Jack on the flagpole, and their anger became rage when they realized that the British had nailed their flag in place and greased the pole. After a few men tried unsuccessfully to scale the pole ande remove the offending symbol a call went out to gather saws wood, and nails. Cleats were affixed to the pole, and a young sailor started to climb, but before he got too far, a ladder arrived, which he used to reach the top, tear down the British flag, and replace it with America's colors, resulting in shouts of joy and a thirteen-gun salute." [punctuation not mine.]