I was having a discussion about this on Flare Forums with some other members, and this is what I think happened:
A member of Flare once emailed Mr. Okuda about the Copernicus, and he replied that he got the ship's name and registry info from a photo by ILM showing the model redressed for Star Trek IV. So I'm assuming that unless the photo wasn't very clear, he saw NCC-623.
So where did NCC-640, which is clearly seen on at least two different shots of the Tsiolkovsky in the remastered TNG, come from, especially when the ship's dedication plaque reads NCC-53911?
(At this point I'd just like to say that this is supposition on my part, and Mr. Okuda is quite welcome to pipe in with the facts if he so chooses
I think that when Mr. Okuda made that plaque, he was assuming that the Tsiolkovsky would be a new model, a ship contemporaneous to the Enterprise-D, since both ships were launched in the same year according to the plaque's info. If that were the case, then the term "Oberth" was never meant to be the class of the Grissom-type ships, and only became that class retroactively.
It's also possible that the VFX personnel weren't aware of the info on the plaque, and changed the registry from NCC-623 to NCC-640 to be more contemporaneous with the Grissom/Copernicus, and that they thought the Tsiolkovsky was an old ship from Kirk's era.
So we're basically stuck with a ship that has two different registries, one on the physical model itself, and one on the dedication plaque (which was what was printed in the Encyclopedia, since Mr. Okuda co-authored it). To muddy things more, in TNG-R, there's a scene with the Enterprise and the Tsiolkovsky flying together where the NCC-640 was digitally replaced with the NCC-53911 registry, but in other shots the old registry is visible
This could also be why later appearances of the Grissom model sported such high registries: because once the Tsiolkovsky set the precedent, Mr. Okuda just followed through with the same registry nomenclature. It's too bad really, because I think NCC-640 would have fit the Tsiolkovsky much better IMHO.