Thanks to one of my "cousins", Denise Bond, who sent me the 1770 census for Granville Twp. Annapolis Co. Nova Scotia, I think we may have a new piece of the puzzle about where our Andrew White came from - he must have been born in Ireland.
This is his household in 1770:
Andrew White 1 man, 3 boys (John, Phillip & Timothy), 1 woman, 3 girls (Mary, Sarah & Susanna), 8 total, 8 Protestant, 7 American, 1 Irish (Andrew), 0 English, 0 Scottish, 0 German & Others.
We know that his wife Sarah and his children were born in MA, so he must be the 1 Irish person in the household.