Chris, just to be clear, the map you’ve found is the same one Alan Boyd linked to and the one I commented on.
As I’ve said, the Mersey formed the boundary between Cheshire and Lancashire and Stockport nowadays, if not then, straddles it. For a family living so close to the river, it would therefore be wise to extend your search into Lancashire/Manchester as it’s quite conceivable that marriages, baptisms etc. took place there.
I think you’ll find that the parish church for anything north of the river, back in the day, was actually Manchester Cathedral and, should you come across St Thomas’ Church, remember that there are two of them - one south of the river and one on the A6 a mile or so north.