In the earlier generations of my family tree, the naming convention seemingly was that the first son of James was named James, so there are many James.
Even though my knowledge of my ancestors stopped at Roy Jessop Laidlaw, my paternal grandfather, Nancy Brown's response to a message I posted on this website extended my knowledge back to James Laidlaw who was married in Jedburgh, Roxburgh, Scotland in 1841, causing me to guess that he was born about 21 years earlier circa 1819.
It is plausible that the James Laidlaw who was married at Westerkirk in 1746, who you posit was Andrew's brother, settled in Cavers Roxburgh.
Do you have information on the Cavers Roxburgh Laidlaws?
How were you able to find information going back so far?