It appears that when ILM redid the registry on the Excelsior
-class starship model that the modelers didn't change the registry on the saucer only. They changed the registry on the nacelles, as well.
In this shot, the registry on the nacelles was visible. It was NCC-2541. It appears that the registry was on both sides of the nacelles.
As many of the shots of the Excelsior
-class starship model were reuses of the original footage shot for "Encounter at Farpoint", I think that it can be argued that there was a NCC-2541 in operation in the mid-2360s.