If the "X" does indeed NOT stand for "eXperimental" but for something the two of you suggest, then how do you explain the NX-Alpha and NX-Beta from First Flight?
Why should those need explaining? They are not registries - they are frivolous callsigns for test rigs, and more specifically for test rigs involved in the project aiming at creating Earth's first eXplorer vessel. They are rather analogous to the AS missions 201 through 278 performed or planned for testing the Apollo Saturn moon shot spacecraft, even though none of those involved the actual final Apollo and Saturn V stack. Or to the various subscale spacecraft flown today in preparation for hoped-for full-scale versions, and often named after the intended end product of the process.
That the NX-Alpha and NX-Beta exist is actually good indication that NX is not
a generic registry prefix slapped on every experimental vessel out there, but a unique project that will culminate in the first-ever NX class of starships, namely the Enterprise
class. Otherwise, a name like "NX-Alpha" would already have been "used up" in the dozens of starship projects that apparently preceded the Enterprise
As for redesignating NX class ships as NCC class ships in the novels, this makes good sense, because the vessels cease to be eXploration vessels in the novelverse. Instead, they become Combat Cruisers.
It is apparently only some time after this point in history that NCC ceases to be a classic naval pennant code and becomes an aeronautics-style national identifier applying to all starships regardless of type... But at that point, NX in turn indeed becomes an indicator of experimental status, deriving from a different branch of aeronautics. That is, NCC seems to be akin to the N prefix of the registry
aircraft in the United States (or G in Great Britain, or OH in Finland, just to name a few and to emphasize that the letter need not obviously derive from the actual name of the operator). NX in turn seems to derive from the X prefix-extension of the type identifier number
aircraft (although USAF actually uses Y for prototypes nowadays, and X is reserved for the sort of planes that will never see any production). It's very confusing - but it's healthy to realize that these prefix letters cannot be plausibly be argued to be exactly analogous to any single registration or identification system in use on Earth today or in the recent past. The usage is a funny mixture no matter what.