OotP Re-Read: And Another Thing

[slowfox]

cynthia_black wondered about who was allowed to touch the prophecy - it's labelled as (?)Harry Potter, when, as Dumbledore reveals later, it could just as easily have been (?)Neville Longbottom.

But, as we established earlier on in the re-read, Trelawney made the prophecy before either of the boys had been born. So...

...when was the prophecy stored in the glass globe? When was it labelled? If it was labelled after it had been saved, then who was able to touch it to label it? And alright, this is just one prophecy, but it's clear that there are thousands upon thousands of these stored in the Ministry, so the logistics of administration are looking suspiciously non-trivial.