You may have solved a problem for me with this, David:
"There were already Armstrongs in Graffham, as a Charles widower married Mary Barton there in 1759"
Charles Armstrong, b 1712 was the son of Thomas Armstrong the JP and his wife Frances Thompson.
Charles married first to Elizabeth Collier, and second to Althamia Priaulx. He had 4 or 5 children with Althamia, all of whom are alleged in Burkes to have died without issue. Althamia appears to have died in 1753, buried in Ampthill.
HOWEVER...
Charles 1750 certainly survived, married, and produced children in Houghton Conquest and later in Graffham - who were the subject of my original query.
AND
A document on BLARS dated 1788 names a John Armstrong as son and heir at law of Charles, late of Houghton Conquest, decd., son of Thomas and Frances. He would have been at least 21 at this time, as he was dealing with leases for land and property, so born before 1767. The document ends with an extract from his will, naming his wife and daughters, and appointing as his executors Charles Armstrong of Wootton (see above, posh lot) and William Armstrong of Hawnes (ag lab lot). I found him in 1841, aged 70, with his wife and daughters.
But where did he come from and who was his mother? Charles' wife Althamia was dead. Given later links with Graffham, the marriage you've found could be a third marriage for Charles b 1712, which produced the mysterious John (and perhaps others?).
Charles 1750 moved to Graffham after 1785 - Charles 1712 died before 1788. It seems possible that Charles 1750 moved to Graffham to take up inherited property there on his father's death, while John inherited the Houghton Conquest/Ampthill land and property.
Hmm. That would account for there being no baptism on the IGI for John b about 1767 nor a third marriage for his father. It begins to fall into place...