Sorry for the belated reply - have been on holidays. Yes,
when I first started family history I was told the name was Welsh and like you, have no evidence to support this! Though my dad and his family were staunch Methodists and also good singers...so I thought that may be where this particular family story came from. It is interesting that you are from another branch and have heard something similar.
Are you descended from Isaac and Mary's daughter Winifred?
My mother's family has a connection with the Parish name - around the Dungog, Paterson, Stroud area of NSW. Any relatives in that area?