The name was not misspelled in the way you think. It was originally McGavocke. And as to the origins in Scotland.. it would have been WAY back. Felix McKillops book, speaking about Carnton, Glenarm, states that " The McGavock family have been associated with this sub-denomination with in the townland of Libbert for centuries". Libbert is adjacent to the location of the town of Glenarm.
I have a bit more information for you about the Glenarm McGavocks.
A new book was released in November 2006 by a local historian Felix McKillop titled Townlands, People and Traditions. It is 300 pages of stories and pictures about families in the Glenarm area. The McGavock name appears throughout.
My GGGgrandmother Margery McCloy was a McGavock. She was born in Munie, Glenarm, Antrim Ireland
in 1757 and died at 103 years in 26 MAR 1860. She Married William McCloy 1746-1813 and both are buried at the McCloy family plot in the old church (church gone) graveyard at Glebe, Glenarm. I have been there several times.
We are reasonably certain the Margery was the daughter of Daniel McGavock born 173?. Daniel, Randal and Joseph McGavock were brothers of James McGavock who emigrated to America. Their father was Hugh McGavock who's father I believe was a Hugh McGavock who was possibly the son of Bryan McGavocke who was in the land records of 1666 for the area.
The book can be purchased directly from Felix McKillop at 21a Aughaboy Road, Aughaboy, Glenarm, Balleymena, Co Antrim, N. Ireland, BT44 0DZ
Felix email address is firstname.lastname@example.org
I hope this helps your family research. I welcome any information you may have about the family.