I think the answer to this question is that either A. The Constitution was not 1700 (as there is no evidence onscreen stating it was maybe 900 or 1000) or B. that the Constitution was 1700 and that each series had its own class name which was never disclosed 1000,1300,1600 etc as Jefferies and Jein seem to indicate in their commentaries making Enterprise series IX DSC. Remember back in the days of the old series there was no thought given to different starship classes looking different from one another. Class could have denoted service specifications. Even the Daedalus did not exist as an idea until TNG times (the model was based on a rejected idea for the enterprise right?). My only issue with this is that old sources claim only like 12/13 connies in existence and I'm sure they were talking about Potempkin, Constellation, Intrepid, etc. with registries lower than Constitution and not some 12 other ships. The third possible option is that Constellation and older ships had been refitted to look like Constitution class starships some time before the original series takes place.
To be honest of the 3 choices I tend to support the simpler explanation that Jein was wrong and that they are all Constitution class ships and that the original connies could have started somewhere in the 900's with the series constantly evolving what the Enterprise actually was as episodes aired. It's been a while was it ever said explicitly in the series how many connies there were? If so that doesn't mean that's as many as there ever were obviously