That could work nicely for continuity purposes, barring the Farragut's actual appearance on-screen as Constitution-class.
And how likely is that to happen considering it's never been shown in forty years of the franchise?
that Kirk served on has been depicted in some comics and described as a Constitution
class in novels. However, since those are not canon, your version serves very well.
Actually, I think your version is superior in this situation. It's nice to see the fleet fleshed out with something other than "Hero" class.