It seems very likely that the man you ask about is a member of the Barall/Barrel family that arrived in Philadelphia in 1754. However, I think it will be difficult to nail down his parents (or even to confirm that he was one ot that Barrall family and not some other family) until you nail down exactly what you know (and don't know) about this man and each of the other inferred family members. In reviewing the profiles for this man and the other people in his inferred family, I see many statements of fact that are not clearly supported by the sources I see.
I appreciate that many members don't like it when profiles are "cluttered" with source citations and similar details. Avoidance of detailed source citations is great for storytelling, but not for research. When trying to nail down the details of a person's life or origins, I find it very important to document exactly what I know from each source and (if there's some uncertainty) why I believe it to be true.
Some examples of assertions related to this man that need better documentation:
- What name(s) is this man called by in each of the records you describe in the profile? In this question, you describe him as "Johann Michael", but nowhere in the profile data, biography, or source list does the name "Johann Michael" appear.
- I notice that this man's inferred father has a brother named Johann Michael, and both "Michael" you ask about and the uncle Johann Michael are identified as having been a "Fife Major" in 1779. What exactly did the record say about this? Is there evidence to tell which one of these two men (birth dates just 12 years apart) was the fife major?
- This profile and the profile for uncle Johann Michael both refer to a will written in 1802. Apparently there were two wills written by two different men in that same year? How can we tell which man wrote each will? The profile for this "Michael" says that no wife is mentioned in the will, but it doesn't indicate what else the will said, and the source citation doesn't indicate where you accessed the will.