I was just going by your point about being able to see the Prometheus's registry on-screen despite it being used as the Lexington. However, I'm content to have Okuda's 61832 registry as the official one.
Alas, with the Discoverse folks set on 30405, and with many other folks also interested in the SB173–SDS registries, the ship of chaos has sailed. 61832 is second only to 30405 in the "hard to justify canonically" category.
After all, the Okuda backstage registries held sway in part because we all (thought we) knew back then that if they ever did actually go to the trouble of showing the ship with registry, or a screen that included it, it would bear the registry that he had given it.
Oops. Even ignoring the Discoverse 30405 thing, examples of Okuda changing his mind backstage do exist. He overwrote Jein's "STAR SHIP STATUS" (SB11-SSS) registry assertions he'd previously championed, for example (e.g. Endeavour 1718 versus Endeavour 1895, Eagle 1685 versus Eagle 956). And, of course, we have other examples like Lexington 30405 seemingly forgotten in favor of the completely backstage Lexington 14427 and apparently contemporaneous Lexington 61832.
So, as it turned out, nothing was set in stone until it appeared on screen . . . which is why that's always my guide, as far as reason will allow.