Nice Topic! 
Take the following just as an opinion Mark.
“La numero 3” is correct because of the envelop which is obviously present even if elided. Number 3 alone doesn’t mean anything. But in “Al coda” or “Al Fine” the part “Segno della” is pleonastic because you want to go just to the Coda or to the Fine… In other words Coda and Fine are an object quite different that the number 3.
My debatable 1ç 
Post Scriptum: I find better “A Fine/Coda” because in this case what is elided is the verb “Vai/Go”