For further information on the Rev Martin and his 5 boatloads of emigrants, try:
Scotch-Irish Migration to South Carolina, 1772: Reverend William Martin And His Five Shiploads of Settlers. Jean Stephenson. Shenandoah Publishing House. 1970.
The Five Ships and the People who came with the Rev. Martin. The names of the emigrants have been reconstructed from letters written home to Ulster and published in the paper and from extractions of the South Carolina Quarter Session Minutes, by Janie Revill and Jean Stephenson; there is a Surname Summary of those who came with the Reverend William Martin.
You’ll see that the 5 ships sailed from different ports and I agree it’s unlikely that many of the passengers came from Larne itself. That was simply a port of departure. No records were kept at the ports of departing emigrants details at that time, and the Rev Martin himself doesn’t appear to have kept any records relating to his passengers’ origins in Ireland. Or if he did, they haven’t survived. Though many of the emigrants are said to come from an area known as the Route, near Ballymoney, in Co. Antrim, they had responded to adverts placed in the Belfast Newsletter, and so could really have come from anywhere in Ulster.