Thank you for looking for me. I took a look at the 1770 baptism for "Anne." Yes, the original image is very unclear! I couldn't really work out the name to be honest. When I inverted the colour and changed the contrast and brightness, the penultimate letter even looked like a V? There was a burial on the very same day for a "child of William Russell." Maybe it was a twin, but if it was "Anne" that might explain why he had another Ann in 1772. There was also another Ann, buried in February 1768. I never found a local baptism for her.
I think the family must have arrived in Sheffield some time before 1752. Perhaps checking settlement examinations / certificates might be the way forward, next time I'm in town and can get to the archives.