I think the first thing that comes to mind on this is "The Valiant", placing it literally 200 years before "Where No Man Has Gone Before" (thus working out to only 2 years after the flight of the Phoenix), when giving it a little leeway for rounding could place it up to two or three decades later. No need for such a tight timetable.
Actually, the Valiant thing is an example where the hands of the Okudas were tied: Kirk specifically says that the ship has been missing for "over" two centuries. In fact, there's already creative license there in the Okuda interpretation as they choose (out of grave necessity) to suggest that the ship was lost almost immediately after she was launched - not necessarily the intent of Sam Peeples.
...there are multiple instances of ships beinig given classes and registries that are entirely conjectural in the encyclopaedia and it's not noted for one
To be sure, most of these are a case of Okuda sitting on two chairs. On one hand, he's documenting Trek. On the other, he's inventing these ship identities for the show itself, and inserting them in Okudagrams on the sets.
The Constitution registries are (poor) conjecture that is somewhat confusingly indicated, but almost all of the other registries and class identities were actually confirmed in elements of TNG set dressing.
Timo Saloniemi