I've followed this discussion with interest, as I do remember the area quite well from, yes, 60 years ago, when I regularly went on the 10 tram to St Mark's Church, Washwood Heath, where my dad was organist.
I don't see any problem with accepting that the picture is of an original stone carved in 1767. Hanson's map of 1778 shows a building on that corner, and I'm satisfied that the stone was built into the new property in the year stated. Like most buildings in those days, it wasn't of the highest quality, but it lasted the best part of 200 years.
The excellent map of 1838 by the Society for the Promotion of Useful Knowledge shows the parish boundary running down that edge of Duke Street, which could mean that the historic boundary line ran a few inches into the corner of the building. Infringements were common, as the Birmingham Street Commissioners had just about been formed, but didn't do much until around 1800.
I wouldn't recommend a wager against my theory, although I have no positive proof.
Peter