The more I look at this, the more I am beginning to believe the Joseph Parrish of Shirley Twp is likely Joshua's father. I went to Fort Roberdeau this past weekend and spoke with a woman there who informed me that it was very common to move back and forth between the frontier and York, PA. Prior to this I could not figure a reason for Joshua moving back east if his family was already in the Huntingdon/Bedford area.
I still have no proof as to this (besides the one random baptismal record noting Joshua's son John as the godfather of Abarilla Parrish McGinnity's daughter, a woman whom history says was raised in Huntingdon Co, PA, again a likely daughter of Joseph).
In the meantime, here's a photo of the plaque on the wall at Fort Roberdeau,