Hi and thanks i think you have found James parents as Stephen and Sarah Baker i checked my old family tree passed down to me and done many years ago and it has Sarah Baker in small brackets (and very small writing).
My guess is that Sarah may have been Stephens first wife and mother to James and Ann Satchell a second wife the dates are right for Stephens birth of 1762 and the first marriage dates.
James (James snr's grandson) and Maria Middleton (nee Reeve) are the only Middletons i have found to have a headstone and its in good condition with lots of scripture on it.
The Middletons and Reeves of Gayton were very close family's living in the same street on the 1841 census and marrying together down the generations my Great grandparents were 1st cousins and there mothers sisters!! i quess this was village life in the 18-19 century
Many thanks again.