Let's say the TOS Enterprise belonged to the Constitution Class. That again negates the "1st bird of the 17th design" idea. The USS Constitution would've been the 1st ship.
What we do have in TOS is the bridge plaque with "Starship Class" and the tech diagram with "Constitution Class" but nothing about Nth design. The Enterprise doesn't get to be the "1st bird" or lead ship until her big moment in TMP and confirmed in TWOK that she's her own class (or subclass of the Constitution Class). That puts suspect to the whole "Nth design" idea, IMHO.
I'm a bit surprised, what happened to your "Thermian" approach?
A) I understood that you base your research entirely on what can actually be seen and heard in TOS. Even in HD the Thermians wouldn't have been capable of reading Scotty's viewscreen schematic in "The Trouble With Tribbles".
This in essentially a behind-the-scenes information (I understood you usually tend to ignore) just as Matt Jefferies' "17th design statement" and The Making of Star Trek
referring twice to (TOS) "Enterprise Class".
B) Let's assume the Thermians would have been capable of reading Scotty's viewscreen schematic, how
would they have concluded that viewing the schematic of a primary phaser of a starship of a Constitution Class is
evidence that the TOS Enterprise
has to belong to this "Constitution Class"?
Again, Scotty is not reading the
technical manual of the Enterprise
but merely a technical "journal", that could show a historic phaser bank same as when Khan was / would have been viewing these materials in "Space Seed". Of course, for him, it wasn't historic but still futuristic stuff he was trying to catch up with.