I bet that gave you a buzz - a recognised artist. I am utterly astonished that the Lincolnshire County Council's arts museum dept. couldn't trace S. Gregory. How could they be so out of touch with how the art world informs itself?
This is my email: firstname.lastname@example.org
No, I am not Poirot but I do have French names which I am not using here. Yes I have worked in professional research (but not as a historian). Bio - keen on the arts; studied fine art; built a small private collection of art, books and antiques; a few years ago I took up painting myself (now over 30 exhibitions etc); long been passionate about history and culture; and have had several books published (various topics). These days I am retired and like to encourage other people with their pursuits in history or family research. Since I am especially interested in combining art and history, your challenge intrigued me.
I'd love to see your painting. It seems that you might have a hitherto unknown S. Gregory. Other things to look at beside the signature and style, are techniques (e.g. brush strokes) and media (paper, paint etc) - as these often contain hallmarks of an artist's work which can be recognised in different works.
There is another thing you can do which is very important for two reasons - establish the provenance. This matters should you wish to have your painting properly valued, say for insurance or estate purposes, and should somebody in the future wish to acquire it. This also might lead you to the artist - and might answer the question as to whether there is a connection to your ancestor Ann. To track and record the provenance - document how you obstained the painting (from whom, when, purchase, legacy, gift, whatever). Then try to find out the history of the painting before that - who owned it, where they got it from, when. If it has never been sold, there might not be receipts or delivery dockets, so just write down the names of owners and how you got it - and especially any folklore. Keep the dockets you would have had from the framers as these are all part of the provenance. Photograph the front of the painting and the back, and take close ups of the signature. This would have been best done out of the frame, so the painting is not photographed through glass - if the frame is sealed leave it alone. Measure the painting (note whether this is the picture alone or includes the frame.
Here's a bit more detective work which might add to the provenance and knowledge of the artist. Check family photograph albums - the painting might be visible in the background of an old family photograph, if so date the photograph and identify person/s and place if you can. I haven't searched for a biography of S. Gregory yet (but will now) - meanwhile assume a survival range for S. Gregory until the late 19th century or early 20th c. Check the family's old photograph albums from this period, scrapbooks, journals, ledgers and memoriabilia if such things have survived -photos, postcards, letters, diaries etc - for anything with the name'Gregory'.
Another question for you - do you know Ann's whereabouts in 1848 - the artist must have been in the same place long enough to paint Ann's portrait.
I am not sure whether a cold Sunday is a cool beverage or refers to the weather; in any case I enjoyed a rather hot Sunday by taking a dip in the esturary expecting it to be refreshing but it was as warm as bathwater.
I am looking forward to seeing your painting Nick.