Well, we never actually see the registry written anywhere (and it probably wasn't). Riker says the E is preceded by a "dash", just as is standard for those ships that actually had their miniatures labeled.
You mean this?
RIKER: It's a Federation ship. NCC one three zero five dash E. It's the Yamato, our sister ship.
Did they originally show the ship with NCC-1305-E and a later DVD version changed it to 71807?