Were they really Constitution class?

The USS Constitution, NCC-1700 is the 'class' ship, as such all Constitution class starships that follow should have registry numbers greater than 1700.

I pose the question;
The USS Constellation NCC-1017 and the USS Republic NCC-1371.  Were they really Constitution class starships?

        {Klingon Academy screenshot}                                         {Starfleet Command 3 screenshot}
                       Side by side comparison of the Constitution (left) and the Asia class(right).

To the best of my knowledge, the Asia class is fan created ship by Bernd Schneider and is older than the Constitution class, the class ship being commissioned in 2204.
The registry number scheme Mr. Schneider uses is consistent with that of the USS Constellation NCC-1017:

USS Asia NCC-945
USS America NCC-991
USS Africa NCC-1002
USS Europe NCC-1003
USS Australia NCC-1004
USS Jefferson NCC-1073
USS Manhattan NCC-1074
USS Yukon NCC-1105
USS Thule NCC-1106

Even though the naming scheme does not.

Both classes have very similar profiles; a large 'flying saucer' style primary hull atop a connecting dorsal, a secondary/engineering hull with pylons and nacelles coming out of it at very similar angles; and from a distance could be easily confused. 
I conjecture that the USS Constellation was;
a) in fact an Asia class starship (based on Registry number) but Desilu/Paramount used the AMT Constitution class model due to budget requirements; or
b) may have been an Asia class refit into a Constitution class and as such kept it's original registry number (much like the several incarnations of the Enterprise).

I bring the USS Republic into this argument sole because it has been assumed by much of fandom that it was a Constitution class ship.  But was it?
Again, I use the registry number as my main point.  NCC-1371.   This would again indicate that the Republic would be of an older class starship yet likely newer than the Asia class.  At the very least the Republic was another class of starship contemporary to the Constitutions.

A large part of the trouble with all of this is that we only have this kind of continuity in registry numbers with the Constitution class starship.  If indeed, NCC does stand for Naval Construction Contract as has been put forth by others, then why are they contiguous only for the Constitution class?   
Shouldn't there have been other types of ships in other construction gantries starting their construction at the San Francisco shipyards that fell in between each of the Constitutions? 

Hell.  All this could be me just thinking too damn much about all of this silly stuff.

Give me your thoughts on this, TrekSpace.