I think Barrett's Privateers is a great song, but hardly suitable. It is a Nova Scotian returning home after fighting the Americans, so it is unlikely an American would be singing it. It also isn't like sea songs of the period I have heard.

I'll stand corrected on this, but I don't think the Americans in 1779 would have crossed Lake Ontario to fight, for the simple reason that there was very little on the Canadian side to fight for. Ontario really wasn't settled until after Loyalists came up after the Revolutionary War. Americans did go and attack Quebec City, but unfortunately for them in a blizzard and they took a licking from the English and the French-Canadians. (They had alienated the French Canadians by not paying for food they took, and the English convinced the French Canadians that the Americans would not tolerate Catholicism.) They did take Montreal at one point and Ben Franklin took the opportunity to introduce the first printing press in Canada. There were plenty of battles around the Great Lakes during the War of 1812, however.

There was some action on the east coast. Washington was unhappy that American privateers were raiding Nova Scotia, as he had hoped to get the Bluenosers to join the cause. The Yankee privateers weren't all bad, though. When they raided Lunenburg, Nova Scotia, they looted the bakery and handed out sweets to the village children.

How about Dark-Eyed Sailor, as performed by Steeleye Span? It is about a sailor who returns and is not instantly recognized by his girlfriend.