Re: USS Copernicus, NCC-640 or 623?
I tend to prefer that myself, as that's often how I've seen registries done in various technical sources. Most of those do seem to have a hint of chronology, in the sense that each batch is usually associated with a specific class and it's unlikely to be reused (though not impossible) outside of that batch. And there are certainly examples of specific registries being shifted around when it was decided to modify the class of the ships being built, as happens in Mastercom's Ships of the Star Fleet.
"If you think you're brave enough to walk the path of honor, then follow me into the dragon's den."