Again, take that with a grain, this is more "closest available proxy right now." Post particular ship requests in the Stats Committee and I'll trawl the data to see what we can come up with as a Playtest Candidate.
From what I see, Essex as-launched is 26x12# plus 16x24#crde, while a typical British 12-pdr 32 fit of around the turn of the 19th Century has four less carronades, more commonly also 18# though the Thames-class (ironically a revival of a 1750s design) were rocking 24's in 1806. Take the best Amazon, boost her Burthen to 3 and give her a slight Gunnery buff, and with American live-oak hulls maybe give her an extra hull box. (Similar for Indian teak.) She's about 10' longer and 3' beamier than her British counterpart, and a hundred tons BM heavier.
EDIT: Apologies for the HUFRACKINGMONGOUS image, but I found this comparison chart of the American 12-pdr frigates...
When taken, the British thought Confederacy's hull would be more appropriate for an 18-pdr 38 or even a small SOL than a 12pdr 32/36! (Interestingly, sister Alliance was outfitted with 18pdr's, implying Confederacy was meant for them too.)
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