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It does seem to be the likeliest explanation, though the original foundling might have an ancestor of your great grandmother. Mark Antony Lower, writing in 1860, informs us that "This name was given to a foundling at Doncaster not many generations since". Doncaster is about 20 miles from East Yorkshire.
The name is also in Cornwall, and one writer suggests that there it could be from a Cornish place name, Penfound. I think it more likely that the Cornish Founds are another family descended from a foundling.