Cary L. Brown said:
It's fine to posit a new explanation, but I'm much more in favor of just sticking with the currently-accepted explanation (albeit still "non-canonical").
The Republic and the Constellation were testbed vessels... each was refurbished to include some portion of the upcoming Constitution-type construction (presumably, one took the saucer, one the secondary-hull). Eventually, both were fully upgraded... ie, the other components were swapped out as well. Essentially, a whole new ship but transformed a chunk at a time and never actually decommissioned and recommissioned (which would have resulted in a new registry number).
That explanation has appeared in multiple places, and is my PERSONALLY preferred explanation. Feel free to come up with your own, of course... but just be aware that there is another, widely accepted, one out there already.