Hello
I, too could not find a Martha Hains circa 1787 of any spelling in Tilehurst. In fact, she could have come from anywhere although the local area is most likely.
I haven't been able to find a burial for Sarah Barnes either, so a search of other local registers might come up with something. I think, from the Berks Burial Index, that she may be the one buried in Tidmarsh in 1824. She is the right sort of age.
As you say, Artifis, the most likely place for any immediate further information would be John Barnes 1871 death cert.
Yours
Vicwinann