Hi
I am not an expert in anyway, however I am pretty sure the USN did not mark the back of issued Tudors Subs. (With USN in anycase)
The only marked Tudors were the MN issued versions from France as far as I am aware.
Ask over at MWR there a more loads of guys who know their stuff and should be able to help. (Just noticed you have checked at MWR).
Lovely looking watch in anycase.
John