Wow! I really outdid myself in goofing this up!!!
Thanks to all of your thoughtful responses, however, I think I've figured it out. Yes, the correct Ann turns out to be Ann Skelhorne (Wright) buried 1812 in Ringstead. Yes, John and Elizabeth are the children of Ann Skelhorne and Thomas Wright. And yes, Thomas Wright died 1826 in Islip.
I think the correct Thomas Wright was born 1778 in Ringstead to Susannah Wright. There is no father listed in the baptism record but it doesn't say Thomas was illegitimate, which is confusing. (The record has been transcribed incorrectly. The transcription says the father is Thomas Wright but the actual document doesn't list a father at all, only the mother and baby.)
The mother, Susanna Wright was born 1750 in Ringstead, and Wright is her maiden name.
What's still confusing is that according to Thomas Wright's death certificate, he was 50 years old so his birth date should be 1776 (rather than 1778). Would it be reasonable to think he was born in 1776 but wasn't baptized until 1778?
Thomas Wright is my 3xgreat-grandfather. He married again in 1816 in Islip to Mary Barker and had three more children. One of those children, George, is my 2xgreat-grandfather.
I think this is the right Thomas Wright, but do you think I should keep looking? There's at least another bazillion or so I could sift through.