Not 100% sure that this is the correct birthdate, but was unable to find anything more convincing. I would have preferred an Edward whose father was Thomas, being as he called his first son Thomas. His second son, John, could have been named after his wife's father. As it is, the best fit for Edward is this one from Adderbury, Oxon, about 8 miles south of Shotteswell and Cropredy, born 28 January 1759. Unfortunately his parents were Joseph (no trace in descendants) and Joyce (also no trace in descendants). The other best bet was born in Birmingham, some 37 miles away, and unfortunately his father is also John, so no Thomas link found there, and there is also the discrepancy with the birth year, 1762 instead of 1758 as indicated in his burial record. A more "local" Buller family would also have been preferred, either in Shotteswell itself or in nearby Great Bourton/Cropredy, or even Banbury. Perhaps this needs to be revisited in the future.
Edward Buller baptised 28 Jan 1759 at Adderbury, Oxon (8 miles south of Shotteswell), parents Joseph and Joyce. m Mary Butcher/Boucher 20 Nov 1786 at Cropredy, Oxon. Died 7 Jan 1832 at Shotteswell, aged 74 (b1758).