Steve- you are a wonder! Yes this is definitely the same song.

Eckstorm says the manuscript came from one John Boyd who was serving in 1759 at Fort Cumberland Nova Scotia .   
The fort was/is located at the headwaters of the Bay of Fundy near what is now Amherst NS.It is now a national park.   
Originally built by the French from 1751 to 1752, it was called Fort Beauséjour. They surrendered it to the British in 1755 after their defeat in the Battle of Fort Beauséjour, during the Seven Years' War. The British renamed the structure as Fort Cumberland. The fort was strategically important throughout the Anglo-French rivalry of 1749–63, known as the French and Indian Wars by British colonists. Less than a generation later, it was the site of the 1776 Battle of Fort Cumberland, when the British forces repulsed sympathisers of the American Revolution.

No doubt, the song was a favorite among the English soldiers there as it celebrates an English victory made possible by the young cabin boy. The date of its presence at the fort may help narrow down the actual event celebrated.

Thanks so much for your research- you seem to have access to a wealth of information!

I will try to contact the Canadian park service and see of they have records of soldiers there in 1759. Maybe we can find John Boyd and his "orderly book"!