I don't know about your baseball playing but I agree. The architecture of the stock is completely different when compared with a Peter Neihart Rifle.
Also, the trigger guard shape is different.
The rail at the rear has a much deeper, more curved shape than those on the signed Neihart rifle. That deeply curved shape was not popular until much later.
Here's a picture of a signed Neihart rifle
And, a picture of a unsigned rifle that is attributed to Peter Neihart
I have several other photos of rifles that are attributed to Neihart and all of them have the same basic shape stock and trigger guard.
I also notice that all of these guns have lockplates which have a pointed rear rather than the rounded shape on Peter Hyne's gun.
I suppose it is possible that a Neihart lock was reused on his gun but I don't think the rounded shape of the rear of the lockplate would have been something the Neihart of the 1780's would have used.
Of course many people can have the same or similar names and I don't doubt that the lock on the gun being discussed could be contemporary with the times.
In any case, his rifle is indeed interesting.