I'd like to think that a "maxed-out" Constitution can match the Intrepid-class.....
Well, in the Star Trek universe I'm not sure ship design counts for a whole lot to begin with; the main differences are the size allowing for more crew. Other than that some ships have more specialised designs with mission pods, or a special stream-lined shape for quantum slipstream and so-on.
Otherwise the hull of the ship is really just there to hold all the important pieces, namely the warp-core, engines, power systems, shields and deflector, which I think an enterprising fleet could absolutely fit into an older ship if they were willing. It wouldn't be an easy job by any means, but there should be enough space to fit everything you need into a constitution class; it's not like we're talking about hooking up 25th century warp cores to 23rd century power systems, but a fully refit of all systems onto what is essentially just a shell for holding it all.
Really the only area to worry about is whether the captain of said refit ship is foolish enough to adopt older uniforms that leave the female crew members struggling to battle-stations in tiny mini-skirts, or the men for that matter if a few episode of TNG are anything to go by?
My main concern with adding more earlier ships into tier V is that it's already a really busy space. It might be nice if some classes of ship were rolled together as equivalent for the sake of simplicity, and simply allow us to choose a basic design for the ship from which we then select individual parts. Otherwise new tier V ships need to have some kind of nich? designed for them which is what leads to a lot of balance issues between ships.