Now I'm baffled. You describe the puncture as being away from the rim side, more like center tread in the tire. So, why are you comparing the location to the rim? I know that it's easy because of the valve, but there's no assurance that the tire is oriented the same way each time, unless you make it so by always mounting a reference of some kind at the valve.

Since the puncture is on the tire side, it's reasonable to assume the cause is there too.

take the time to examine the tire carefully, flex every little nick open until you can see clear to the bottom and verify that there's nothing embedbed there.