That does seem to be how they number ships, but then you have the Enterprise NCC-1701-J which is from the 26th century. That's well after they went to the 5 number system. None of this stuff is written perfectly though.

To me, it looks like a bit like a Klingon D6/D7 body combined with an Excelsior or Centaur class saucer section. (Since the Centaur was a combination of Excelsior and Miranda class ships, I guess that's a little redundant).

I wonder if the tone of music is supposed to mean anything?