It doesn't make a lot of sense IMO to take the saucer section of a Saladin-class ship and make a new Contitution-class vessel out of it. After all, despite outward similarities, the interior components and layout of a Saladin-class and a Constitution-class saucer have to be vastly different since the shuttlebay, main deflector and warp engineering (plus at least some of the cargo holds) on a Constitution-class ship are in the secondary hull which doesn't exist on a Saladin-class. You could make a case that a Saladin-class doesn't carry shuttlecraft but warp engineering and the main deflector are non-negotiable. From the episode, we can tell that main engineering on the Constellation
is very similar to the Enterprise
(notwithstanding the revisions to the Engineering set which took place between Seasons 1 and 2). To convert a Saladin saucer to a Consitution-class would involve a lot more than just plopping it onto a waiting secondary hull, you would have to gut out most (if not all) of the interior of the saucer. It would make much more sense to construct a new saucer.
Also, in the original Technical Manual, all Saladin-class ships have 3-digit registry numbers starting with NCC-500, so NCC-1017 doesn't really fit into the Saladin-class any more than it does the Constitution-class. I agree with the theory that NCC-1017 was a re-use of an old registry number after a previous Constellation
They should have just gone with NCC-1710. Yes, TV screens were much smaller in the 60s than they are today, but we only saw the registry in one shot and the different name, plus all the damage, should have made it pretty clear that it wasn't the Enterprise