I'm also curious to see how it went from NX to NCC and why...
The "NX" designation is generally used for experimental vessels, test platforms for new technologies. The first time we ever saw the designation was in The Search for Spock, where the Excelsior as a transwarp testbed was designated NX-2000. But when we saw the Excelsior years later in The Undiscovered Country, equipped with standard warp drive, its registry was NCC-2000.
I for one see no reason to assume that "NX" has the same meanings in the Federation vs. United Earth Starfleets. For the UESF, "NX" was a class of ship -- NX-class ships receiving a numerical designation in order of production. Presumably, other classes of UESF ships had other letter designations -- perhaps there's a YF-class starship, for instance.
So the paradigms -- NX-class vs. [Ship Name]-class; numerical registry for a particular class in order of production vs. general registry of "NCC" and testbed ship registry of "NX" -- seem completely different between the FSF and UESF.