I agree that you have "almost certainly" (meaning about 99+%) proven that Patrick Jr remained on the Island. I don't think anything more could be found which would sway that opinion one way or another.

I think it is possible that the illegitimate Patrick left the island; that, too, would take more investigation and perhaps nothing definitive would be found.

You are to be commended for your diligence in investigating, and untangling, this family, and many others as well. Your contribution to Manx genealogy is inestimable, and I, along with many others, am very grateful.

One of my pleasures in genealogy has been the wonderful, sharing, community I have found on this board, and the way in which, inevitably, one gets back so much more than one has given. You are a big part of that. Thank you!