I don't see any evidence that would indicate this James Woodrow has anything to do with Thomas Wodrow at all. To the extent he does belong to "that" Wodrow family, it seems more likely, given the naming conventions, that his father would be Johne born 1662. From there, we could at least posit that this is the son of John Wodrow born 1630, whom the Wodrow biography says was executed in 1666 for demonstrating with the Covenanters. If so, then James's father John would likely be the Quaker that the family seems to have disowned, and might have named his son outside the tradition as a gesture of defiance.