I had a thought. Based on "The Case of the Jonathan Doe Starship", I would assume that the ships listed on the chart of Starbase 11 are Constitution class starships. And this supposition is going to be as lacking in basis as that article, but it has been influential on what became ship numbers in TOS-R. And this is going to be flawed and based on quick observation. So here we go.
Removing the numbers that have been assigned to Constitution class starships leaves us with the following numbers: 1831, 1864, and 1718. Greg Jein misread this as different numbers (1631 and 1664; heck, I could be misreading 18/664 myself), and in the case of 1718, this number was intended for the USS Endeavour, but this ship was later given the designation of NCC-1895 in the canon. It is therefore a free floating designation. Of these, NCC-1831 is at 100% completion, NCC-1864 is nearing 80% completion, and NCC-1718 is at 45% completion. If we assume that in this case, "complete" represents construction, and that it takes at least a year for a Constitution class to be built by this period, then this would indicate that these ships had to have begun construction in 2266. "Court Martial" was first aired in February 1967, but was filmed in October of 1966, and if episodes were aired in production order then it would have aired in December 1966 as the 14th produced episode in lieu of "Balance of Terror". Regardless, it takes place in early 2267, so we can assume sometime in January or February of 2267. So construction on NCC-1831 would have had to have taken place in January or February of 2266, NCC-1864 some months after that, and NCC-1718 several months after that. So that's three ships under construction throughout 2266, into 2267.
Assuming a year for construction of each, each should be completed in 2267, and certainly not before the latter part of the year when "Tomorrow Is Yesterday" would have taken place. Assuming a year for launch and then another year for commission, these would be three ships launched by 2268 and commissioned by 2269. Depending on timetables. I am assuming a year for launch and a year to commission, but after construction is completed, it could be considerably less. That is all assumptions based on the giant assumptions I am already making in this thesis.
So based on this theory, it is plausible for three Constitution class ships to be constructed a year, beginning in 2266. If we assume it takes two to three years from construction to commission, that would mean ships begun in 2266 would be commissioned by 2268/2269, 2267 ships would be commissioned in 2269/2270, etc. I would assume (again, in this vast sea of baseless assumption) that they would stop with TOS Constitution ships when they got to the point of the massive refit, which began in 2270 or 2271, and not make flag ships for a five year mission that were soon to be outdated. I would assume they would want them back by 2273 to 2274 at the latest. So I think it would stop at about there, making for around an additional six possible Constitution class starships in the TOS era before it is over.
And again, this is totally baseless speculation. You could drive an 18-wheeler through my logic, and easily point out something I misread or did not read. But then again, so was "The Case of the Jonathan Doe Starship".
EDIT:
I forgot to include the USS Eagle. Greg Jein assumes it is NCC-1685. However, it was later mentioned in canon as NCC-956. We can get into the convolution of NCC designations, but what this means is that it is another free floating number. Going by the same logic, we can assume it is a Constitution class ship under construction, which is a little over 20% completion. So that lines up with a concept of ships beginning production, one after another, with a distance of several months until production starts on the next. This also means 4 ships rather than three beginning construction in a year. And therefore, by my logic, it would be around 8 rather than around 6 Constitution class ships that could be constructed in the TOS era.
I will also amend the theory with the idea that there may not be a difference between launch and commission in Starfleet. It may be that as a ship is nearing completion or shortly after completion, a captain is assigned, chooses his crew, and the ship is commissioned. This would remove a year from the theory, and crew selection could only take a period of months if it occurs after a ship is completed rather than as a ship is nearing completion. I use the example of the Enterprise-B as the basis for this theory. The ship had a captain and crew when it launched and appeared to be commissioned. They had the space champagne and everything. However, it was missing equipment, which is the sign of a launch prior to naval commission. Therefore, launch and commission appear to be synonymous in Starfleet, or at least there is the possibility that they are. So again, this shaves off a year in the theory. Therefore, ships constructed in 2266 could be commissioned in 2267/2268, 2267 commissioned in 2268/2269. However, if ships were built beginning in 2268 and launched in 2269/2270, that would place them right in the era of the massive refit and they would return for refit only in 2274 to 2275. We could argue Starfleet would already have begun updating these ships such that they are a bridge between the original design and the advancements of the refit and the refit is easier, but that complicates the theory. I would therefore assume that it would only be only 8 ships.
Of the 14 ships in the season 2 production list, the USS Constellation was destroyed in 2267, the USS Defiant was lost in 2268, and the USS Intrepid was destroyed in 2268. The USS Farragut was never officially mentioned as destroyed, but there's indication it may have been. And for the "12 like it" statement to work, I assume the USS Valiant was destroyed prior to 2267. The USS Defiant complicates things, because it was not on the list of 14 ships. So I will set it aside for the moment. So if we assume 13 Constitution class ships, at least three of which had been lost, and add that 8, there are 18 Constitution class starships.
There is the complicating factor of the following three ships not being part of the list of 14.
USS Defiant (NCC-1764)
USS Eagle (NCC-956)
USS Endeavour (NCC-1895)
I do not know how to properly treat these three. If we just add them on, no questions asked, and with the USS Defiant lost, it would be 20 ships. Perhaps we can assume the Defiant was not yet commissioned as of that statement in 2267, and therefore would be in the pool of ships under construction.
After all that, I have a headache. There's 17 of the 12-13 Constitution class starships? Jee whiz. Someone make
that logic work.