Baille Mor = city ( Large town). Adjectives normally follow nouns, adjectives can go to the front if the adjective is emphasized.
It may also have been a nickname for someone of dark or swarthy complexion, deriving from the Old French "more", dark-skinned. There was also a personal name of the same origin, which was borne by several early saints. The given name was introduced into England by the Normans, but was never as popular in England as on the Continent. In Ireland the surname originated as an Anglicized form of the Gaelic "O'Mordha", composed of the elements "O", descendant of, with "Mordha", a byname meaning great, proud, or stately. In Scotland and Wales it was a nickname for a large man, deriving from the Gaelic "mor", Welsh "mowr", big, great.
anyway lowland scots have their origins as celts but have become much intermingled with many other peoples of different ethnic origins.
nobody has , unless i missed it, given any evidence that the south was primarily of anglo-saxon decent. trying to tie it to scotch-irish immigration doesn't cut it.