Looking at Bingham baptisms, I wonder whether Amy was always known as that. John of Horsted Keynes seems to have also had partners called Emma and Emia, so perhaps Amy could be buried under one of those other names. What children do you have for them?
I found a birth of William to John & Amy, in 1801, but think the following are also worth your consideration.
John (1796), Philidelphia (1797) who had a mother Emme/Emia, and two other children born to John & Emma were baptised on the same day but late. Allen age 9 in 1818 (born 1809) and Mary age 15 also in 1818 (born 1803)
There is a rogue entry for a Sarah born to John and Philidelphia(?) in 1799 which you may also like to think about.
If Emia/Emma were other names for your Amy, she had to have died post 1809, and if its the same John remarrying in 1827, that narrows down the search for Amy's death even further.