Thank you David and David for your excellent suggestions.
I've used the surname search on all my great-grandfather's lines, and found no meaningful connections: none at all for his mother and both grandmothers' rare names, and no obviously pertinent matches for his own extremely common surname.
I also tried searching in the 'place search' for the main areas in his ancestry, and again received negligible results.
Of course, I've also looked into those without trees (who wouldn't come up on such a search as I understand), and none of those seem relevant.
Anther point is that I know there is an American mormon distant branch on that side, who are very involved in genealogy and I was expecting to see them come up in my matches.
In short, I've yet to come across any match that I can say matches any lines of that great-grandfather's family.
As for your question, it's mostly based on looking at their trees (the ones that have comprehensive ones), as well as my own research into their trees (eg the ones that only go back 1-2 generations). When tracing these back, I was astounding to keep coming back to the same names and places, eg the "Smythe" family.
I have contacted the closer connections, and only 2 have replied, one we can't find the connection as their paternal side is unknown, and the other, has a comprehensive tree in the same vicinity as the "Smythe" family, with a potential link in the mid-18th century.
I would very much like to hear how you would continue to approach this, what the steps would be. So far you've both given me such guidance and much to work on.