Here is an exerpt from "A Crawford Genealogy" page 4.:
Hugh Crawfurd died in 1576, and was succeeded by his son,
1.Sir Malcolm Crawfurd, of Kilbirnie, who married Lady Margaret, daughter of John Cunningham of Glengarnock, and, by her, had two sons:
1. Sir John Crawfurd, his heir.
2. Alexander Crawfurd, of whom there are no descendants.
3. A daughter, married to William Cunningham, ancestor of Sir William Cunningham, Baronet.
Malcolm Crawford died in 1592, and was succeeded by his son,
1. Sir John Crawfurd, who, in 1600, got a charter, under the great seal of the lands and baronies of Kilbirnie, Easter Greenock, etc.
Of this line, in 1600, was born John Crawford, who emigrated to America in 1643. From him are descended all the Crawfords of the Kilbirnie branch in this country. Before giving, however, the record of his descendants, we will trace the English family down to the present period.
As stated above, Sir John Crawford, in 1600, got a charter, under the great seal, of the lands and baronies of Kilbirnie, Easter Greenock, etc.
He married Margaret, daughter of John Blair, of that ilk, by whom he had three sons, and two daughters:
1. Sir John Crawford, his heir.
2. Malcolm Crawford of whom there are no male descendants.
3. James Crawford of Knightwood, of whom there are no male descendants
4. Margaret Crawford, married to Hugh Kennedy of Ardmillan.
5. Jean Crawford married first to John Lindsay, of Blacksolme, and secondly, to John Buchanan, of Drumiekill.
While our John Crawford of Jamestown is NOT "Sir John Crawford, his heir" i.e. John Crawford of Kilbirnie, he appears to be descandent of Hugh Crawford. And a contemporary of John Crawford of Kilbirnie. Both being born around 1600. Making both of them great-grandsons of Hugh.
They never give the names of John Crawford of Jamestown's parents. Here's what I did on my home database. I put two "unknown Crawfords" in as his father and grandfather, and connected them to Hugh. That way, even though I don't know the lineage, I have acknowledged the family relationship.
Maybe, someday I'll be able to fill in the names .