What this source establishes
The second outside leg, and the one that carries the DATE. Hardgrave is writing the social history of the Nadar community from its own sources, with no interest in this church at all — and he independently gives 1680, a woman, and the 1685 church. Between him and Bayly the shape of the founding stands outside the parish: a woman, a cross, 1680, and a village that grew around her. What remains the parish's own is her name, Santhaayi Ammaiyar, and where she came from. Note also what he does NOT say: nothing here about a priest on horseback, and nothing about de Britto. We do not hold the volume — quoted at second hand, and still in copyright.
This is as much of the book as this site prints. It is named in full in the bibliography below.