I think that the 17th design/1st ship model would be cool in a really planned out universe. In the sprawling verse Trek became, it doesn't work.
I figure the Constellation was refitted as a testbed, ala SOTSF, as was the Republic, hence the non-17xx numbers. The 16xx numbers would have been Baton Rouges that were supposed
to be decommissioned in favor of 17xx ships that were planned/authorized (the FJTM list), but due to the Four Years War, they blocked that decom, and over time, some of those ships were refit to Constitution specs. For the stories I'm writing, I assumed that the Excalibur was a refit BR, 1664, and the 1705 was not built when it was originally planned. When the 1664 was scrapped after the M-5 incident, the contract for 1705 was dusted off and went into production.
This allows for FJ and Jein's list to coexist in a way that makes sense to me.