Thanks, Roger. No joy on finding other parish registers in the area that are available to read online (I've checked Lydiate, Aughton, Sefton, Formby), but the links are nevertheless a great resource. I really appreciate your help.
And Radcliff, many thanks for your responses, too. My male Balshaws are mainly Williams, Thomases, and Johns. They do seem to have used the same given names over many generations. One of my Williams married Anne Goore at Altcar in 1777.
Does anyone know anything about Goore Balshaw? He was the son of William and Anne and appears to have been convicted of manslaughter in 1809--yet sentenced only to six months in prison. I'm trying to discover the story of this crime and the reason his sentence was so light.