You are so wrong it's laughable.
It's Rate not Rank.
The Rate system is a whole lot simpler than what you just suggested, the variation within what you called Brig, Sloop etc that are currently 7th Rates would make your head swim.
USS Constitution and her sisters were super or heavy Frigates they were not built to be line ships and never took on a 3rd rate the only one that came in sight of a third rate ran and was crippled by HMS Endymion, to counter these ships the Admiralty planned to build more Endymion frigates and more heavily gunned super Frigates but as the war of 1812-15 was won they were never needed.
For the purposes of NA Rating USS Constitution and her sisters is very difficult because of her uniqueness but in my opinion she should be better placed at 4th.