I’VE FIGURED IT OUT.
In the Eleventh Hour, Rory’s badge reads:
Rory is 30ish during the Angels Take Manhattan episode.
He’s (presumably) sent back to 1938.
1990 - 1938 = 52 years, 52+30 = 82 years old
The date the badge was issued is the day he died.
Holy Mary, mother of fuck.