I think I might have found something from "Crawford Genealogy"
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, (your John Crawford of Jamestown) 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.
Sir John Crawford died in 1622 and was succeeded by his son.
1. Sir John Crawford of Kilbirnie, who married Lady Margaret Cunningham, daughter of James 7th, Earl of Glencairn, and, by her, had two sons, and two daughters:
1. Sir John Crawford, his heir.
2. James Crawford, who died unmarried.
3. Ann Crawford, married to Alexander Cunningham, of Corsehill.
4. Margaret Crawford, married to Colonel William Crawford.
The older son, Sir John Crawford, succeeded his father, and was created a Baronet by King Charles I. He commanded a regiment of foot in the Civil War, but lived in retirement during the Commonwealth. He represented the Shire of Ayr in the Parliament of 1662. He married first, Margaret, daughter of Robert, Lord Burleigh, by whom he had no issue; he married, secondly, Magdalene, daughter of David, Lord Carnegie, and, by her, had two daughters:
1. Anne Crawford, who married Sir Archibald Stewart of Blackhall, Baronet.
2. Margaret Crawford, who married Patrick, second son of John, 14th Earl of Crawford, (another line) of whom were descended the Viscounts of Garnock, whose title, in 1 749, merged in the Earldom of Crawford and Lindsay, to which George, 3rd Viscount Garnock, then succeeded.
Sir John Crawford, (my John Crawford of Kilbirnie) dying without male issue, the Baronetcy fell to his heir male descendant of Capt. Thomas Crawford, of Jordanhill, the youngest son of Lawrence Crawford, mentioned above.
So where does that leave us? John Crawford (of Jamestown) descends from Malcolm, but none of Malcolm's male descendants seem to have fathered him.
Suppose none did! You will notice that Margaret Crawford was married to one William CRAWFORD. Maybe THEY are our missing parents?