The Armstrongs' arrival in Riseley is still a subject of much concjecture, Richard. Y-DNA shows I share a common ancestor at some point, probably in the 15th to 17th centuries, with two descendants of Sir Thomas Armstrong of Rye House Plot fame. (Sir Thomas was hung,drawn & quartered on the orders of Judge Jefferies, then posthumously pardoned!). Sir Thomas was a friend of Lord Russell, a son of the Earl of Bedford, who was also executed. It may be that my Armstrong ancestor came south from Cumbria with Sir Thomas' entourage. The Rye House Plot was centred on Hoddesdon, Herts. I'm awaiting further DNA evidence which should help narrow down a little more precisely when we interlink.
I have lots of links to Scots-Irish Armstrongs, & know of many who went from the Borders to Ulster, & then headed south to Co Offaly etc. Some then crossed to Bedfordshire.
Another thought was that we arrived in Beds due to the Earl of Bedford. In the 1560s, Elizabeth I sent the Earl to the Borders as a Warden of the Marches. He came into contact with Armstrongs when there. The first Armstrong christened in Beds was in 1586 at Woburn - seat of the now Dukes.
It may also be that an ancestor was a Covenanter prisoner, & worked on the Fens. An Earl of Bedford was partly responsible for organising/funding Fenland drainage etc.
There are a few other less likely possibilities, but I won't bore you to tears!
Re DNA: As you know, Y-DNA is solely father-to-father, so ideal for standard same-surname genealogy. mtDNA is mother-to-mother, so a less focused approach involving numerous surnames!
I'm also trying to prove our pre-surname origins. The most likely options are Brythonic Celt, Anglo-Danish or Norman. I've seen documents mentioning Armstrongs working alongside Normans in Cumbria in the 1230s.
Cheers,
Bob
