Actually, we do not know from TOS (!) whether some of the starships you listed there actually belonged to the Constitution Class (as this is merely a conjectural assumption and better suits those that begin with an NCC-16XX prefix, IMO and for a number of reasons).
Where you have my undivided attention are the NCC-registries of "NCC-1864" and NCC-1897" from the starship status chart in "Court-Martial".
While HD resolution clearly reveals NCC-1631 to be erroneous (as it most definitely shows NCC-1831) I'm still very uncertain regarding 1X64 and 1X97.
Depending on which moment I freeze frame the Blu-ray image it reads either "16" or "18".
I thought we'd have to wait for 4K UltraHD resolution before we could finally determine what it actually reads.
Why is that important? If it is 1664 for the Excalibur
, 1764 for the Defiant
and 1864 for the Reliant
we could speculate that the last two digits are only a contact code a new ship will "inherit" from a deceased ship.