Agreed with most of the above. As convenient as it is to make NCC 'Naval Construction Contract' it just doesn't make sense. The 'Navigational Contact Code' idea holds more water, IMHO. I would prefer to believe the three letters don't actually stand for anything and like you suggest just collectively indicate that it's a Federation Starship.
However, regarding the AMT kit, I would urge you to consider that it is also possible that the AMT kit specs are merely the closest that the Constellation
and her stablemates could be upgraded to Bonhomme Richard
specs or whatever you want to call the Enterprise
subclass, and the differences are a result of their radically different (Baton Rouge
?) original design.