Actually, the Greg Jein numbers assigned from the wall chart in "Court Martial" should be disregarded, on the simple fact that it would be completley unreal to have almost the entire Constitution fleet at Starbase 11, unless Starfleet's Deployment Staff is run by monkeys.
The only "canon" Connie numbers are the Constittution's (1700), the Enterprise's (1701), and the Defiant's (1764, though this particular number is only from a status sheet that was made during production, and hasn't been avalible in recent years.) Literally all other numbers for the Constitutions are conjecture, though it is possible that the Lexington was there too (being NCC-1709, and fitting into the standard registry scheme established by the Conny.)
I think that the Republic, along with possibly "other" Constutitons are actually members of an older Starship class, as I sincerely doubt that Starfleet has that few Starship designs avalible. Additionally, it's pre-Conny registry would invalidate it, and would be best assigned to something similar to the Baton Rouge Class from ST Chronology.
From canon evidence, my own conclusions and analaysis of the episodes, I have established the following ships as Constitutions.
Constellation
Constitution
Defiant
Enterprise
Excalibur
Exeter
Hood
Intrepid
Kongo
Lexington
Potemkin
Yorktown
Amazingly, this makes for a total of 12 Constitutions in TOS, which is makes me pretty happy.
However, TVH shows us that there was a
second USS Intrepid (mentioned in script, cut out,) along with atleast 1 other Enterprise-class ship, both of which are seen in Spacedock with the E-A and Excelsior. Additionally, there is the small problem of the Constellations registry, which can actually be explained quite easily. The Excelsior NX-2000 was comissioned in the 2280's, but in TMP, the USS Entente NCC-2120 is mentioned as being active. Now, that means that the Excelsior was given her registry
before her construction began in the 2270's, perhaps even earlier if one considers the amount of R&D her Transwarp drive would need.
What does this tell us? Well, the next known Excelsior is the USS Repulse NCC-2544, which should have been around since the late 2280's. Apparently, there is a registry assignment gap between the first and second Excelsiors. I extrapolate that there is infact a
second prototype USS Constitution (NCC-1000, which is althogether fitting once you consider the Excelsior's registry; the next Starship class), in addition to the one we know.
Here is my "corrected" Connie/Enterprise registry list, which includes the second Intrepid and Conny. (This is also the one that I use in my SFC shiplist)
||1000 Constitution
||1017 Constellation
||1700 Constitution
||1701 Enterprise
||1702 Potemkin
||1703 Hood
||1705 Excalibur
||1706 Exeter
||1709 Lexington
||1710 Kongo
||1711 Farragut
||1717 Yorktown
||1764 Defiant
||2131 Intrepid (built as an Enterprise)
||1701-A Enterprise (originally the refitted Yorktown)
I hope this theory helps some of you.