Not connected with the DNA matches, but I found this 1841 census entry:
https://www.ancestry.co.uk/interacti...&usePUBJs=true

Brick Yard, Chippenham, Wiltshire
Peter Griffen 45 Excavator N
Jane Do 50 N
Sarah Sage 20 N
Samuel Do 14 N
John Slush 40 Excavator S.

and then in 1851, they are the household before the Street family in Dundry, Somerset, with Mary Street being a married daughter of William and Jane Sage:
https://www.ancestry.co.uk/interacti...cklabel=Return
Peter Griffin Head Mar 57 Labourer on the Waterworks Devon Columpton
Jane Griffin Wife Mar 61 Do Wife Somerset Long Ashton
Henry Langdon Lodger Widower 36 Labourer Devon Exminster.

"Later" turned out to be a long time later, but at last I know the answer to that one!

A new DNA match appeared at the weekend near the top of the estimated 4th cousins, who is descended from Mary Sage, another daughter of William and Jane, so I think there is enough evidence now to put William and Jane into my tree as Ann's parents. At last!

And other DNA matches suggest that Ann was related to a James Sage born about 1749, maybe in Shepton Mallet, who was transported to the US in 1773.