Looking for May Mays Mayse Nz from Ireland

Looking for information about Alex b.abt.1847, & John b.abt.1849, MAY or MAYS of Co.Tyrone, who arrived in Auckland on the "Dover Castle" 14.8.1875, as Assisted Immigrants. They were carpenters. With them was their sister Elizabeth, b. 1854/5. Their father's name is given as Alexander Mays on her marriage record, and Mayse elsewhere. She married Henry HINTON in 1877, and the family seems to have stayed in the Waikato area. Other descendant names connected to this family:- HALL, HENWOOD, BLAND/WALKER, WHITAKER/JONES. The name Alexander suggests they might be of Scots-Irish origin.
I would be interested to find if they stayed in NZ, as I have found 2 records in USA which could be them. I would also like to be able to fit them into the ongoing World DNA project for all the May surname variants.