In regards to the the second point--If the broadside versions crossed the Atlantic to America later- why didn't they show up in the British Isles? Where are the traditional versions of Gosport Tragedy from Scott, Motherwell and the collectors? Only Buchan published a version which looks to be directly from print.
It would be hard for the Stockton ancestors (or whoever brought the ballad) to bring a ballad over that was not current.
Could it be that the Gosport ballad died out in the Bristish Isles and the shortened later broadside "Polly's Love" entered tradition where it was collect in in the late 1800s and early 1900s?