This is less sure, but the Atlantis from "Conspiracy" might have been an Excelsior-class Starship. This is based on the fact that a diagram of this class appeared in the mission orders for this ship. Well, anyway, this ship had a registry of NCC-72007. So, it's possible that Starfleet was still making these ships as late as the 2360s.
I wouldn't put too much stock in those Conspiracy displays. The diagrams used were just random images that had no connection to the text. Two other diagrams, completely different from the Excelsior, also appear under the Atlantis entry. Plus, the ship's registry on the Starship Deploy Status chart is 32710.
DS9 had the opportunity, when they switched to CGI, to create new ship classes for the battle sequences. Instead, they simply created new models out of the existing models and added a few designs from ILM. So, there must have been a reason, other than budget, that the producers decided to reuse the old models.
There was. ILM was ordered to give up all their CGI models used in First Contact to Paramount for remapping. This included not only the three new designs (minus the Norway, as the CGI mesh was lost), but also Nebula and Miranda low-poly models used in the film, which was why we see them in the DS9 fleet scenes. As to why we also see the Excelsior, that was because they had easy access to Greg Jein's model built for VOY's "Flashback" and could scan it into a CGI model (which is also why we don't
see any Ent-B-type refitted Excelsiors as CGI models).
So it was easier to remap all the FC models and scan Jein's Excelsior than to create all new CGI designs. However, this brings up an interesting thought: If DS9 is ever remastered in HD, will all those CGI fleet scenes have to be redone? And if they are redone, will the same ship designs be used?