I have a list of McCulloughs who arrived in upstate NY. All looked Irish though at least one family was from Connecticut. Mullybrach and Toberhuney, Co Armagh near Lurgan and Magheralin townlands like Kilfullert and Dollingstown had McCulloughs. Presbyterian John McCullagh had Mary baptized in 1754 and Robert McCollugh had son Richeson born Oct 5, 1763 in Lurgan, Co Armagh. The spelling will vary from McCulla to McCulloch, but I don't know if McCollum?mcCallam is a variation.
Many of the dates I have go back as far as 1840 births, however, I have a gravestone of Samuel and Mary "late of Portadown" and children who were buried at Seagoe graveyard around 1817, 1815, 1819,and 1830.
Do you have a religion or family names which could guide a search?