The ballads you mention, Brian, should be compared with published versions from the 18th century and the early 19th. Not all of those who emigrated were poor or illiterate. Some of us still have this idea in our heads that it was only the unsophisticated who carried these ballads. That is far from the truth.

3 possibilities other than the usual.
Some emigrants had learnt them from published sources before they emigrated.
Some took the published materials with them.
Some had them posted over after they had settled.

Remember it takes very little time for a ballad to get into oral tradition from print.

The reason why Duncan and Greig were able to collect many Child Ballads is quite a few were heavily influenced by those published in the early 19thc. Some of Peter Buchan's 'eked out' versions for instance.