Well, here's another interesting subject. I don't have the Takakjian book; I did find a reproduction of the Stevens plans in the CD-ROM edition of the Nautical Research Journal.
My approach to problems like this is always to get back as close as possible to the original sources - which, in the case of early American sailing vessels, generally aren't numerous. So far as I can tell there are two genuine contemporary pictorial representations of the Essex. The designer, William Hackett, drew a set of hull lines, which are in the National Archives. And Joseph Howard, apparently an amateur artist (and son of the sailmaker who supplied the Essex's sails) did a rather naive but intricate watercolor painting of her, probably right after she was launched in 1799. As I understand it, all other representations of the ship are based (directly or indirectly) on those two sources.
I have in front of me a remarkable book called The Frigate Essex Papers: Building the Salem Frigate, 1798-1799, by Philip Chadwick Foster Smith. It was published by the Peabody Museum of Salem (now the Peabody-Essex Museum) in 1974. (A few used copies are available on the web, but they're priced above $50.00.) The frontispiece is a nice, color reproduction of the Howard painting, and there's a photographic copy of the original Hackett drawing folded up inside the back cover.
The Hackett drawing is disappointing. He apparently was, at best, a mediocre draftsman (and a borderline alcoholic). The drawing looks like it was whipped out in an afternoon to satisfy the requirements of the bureaucrats in the Navy Department; it may or may not have actually been used in the building of the ship. It's awfully crude, to say the least.
One nifty feature of Smith's book, though, is that it contains yet another set of plans, drawn by William A. Baker. He was a professor at M.I.T., and one of the premier scholars in the history of naval architecture. (Among his other credentials, he designed the Mayflower II.) Baker traced, elaborated on, and filled out the Hackett drawings, making use of the fantastic wealth of material Smith had dug up about the ship's rigging, spar dimensions, fittings, etc. to do a pretty thorough - and, to my eye, believable - reconstruction. He also took pains to ensure that his plans matched up with the Howard painting.
John Stevens was a deeply respected draftsman and ship model designer who worked, I believe, in the 1940s and 50s. His plans of the Essex are dated 1952. The format I have them in makes it awkward to compare them with the Baker set, but they generally look pretty similar.
Howard I. Chapelle, sugar-daddy of the history of American naval architecture,
also did a set of Essex plans for his History of the American Sailing Navy. He was a little vague about his sources, but I think he mainly used the Hackett drawing and the Howard painting.
Now to the nitty-gritty. The Hackett, Baker, Stevens, and Chapelle drawings all show six ports per side in the quarterdeck bulwarks. The Howard painting shows five, but it's barely conceivable (barely) that another one is hiding behind the foremost main lower shrouds. I can't comment on the other discrepancies Mr. Morse has noted, since I don't have the Takakjian plans.
Portia Takakjian was a fine draftsperson and writer. Her book on the Essex is part of the Conway Maritime Press "Anatomy of the Ship" series, of which I'm a big fan. I do think, though, that the format of that series is better suited to twentieth-century warships. Such detailed coverage of sailing vessels requires a great deal of reconstruction and guesswork. I suspect that may be what's going on here. (I also recall as series of articles Ms. Takakjian did about her model of the Essex for one of the other magazines. She raised some hackles with some highly questionable reconstructing.)
It's entirely possible that some of the features in question actually did change during the course of the ship's life. We know that she got extensively re-armed (almost exclusively with carronades) before the War of 1812; I suppose it's conceivable that the quarterdeck bulwarks got rebuilt at that time. And the Smith book includes some notes made by the naval constructor James Fox regarding a large repair job that was done to her in 1809. Among the changes Fox noted were "shortening the length of the counter" (which might imply a change in the rake of the transom), "increasing the size of the Gundeck Ports 2 Inches," and "giving a Tier of Air Ports fore and aft."
If I were building a model of the Essex, I'd start out by getting hold of the Smith book (they just might have one for sale at the museum) and the Baker drawings therein. By the way, the Peabody-Essex Museum has (or did the last time I was there) a beautiful model of the Essex that was built shortly after Smith's book was published. I don't recall the builder's name, but I'm inclined to regard that model as the most definitive reconstruction of the ship.
Incidentally, the voluminous documents quoted in Smith's book include some letters about the purchase of medicines for the ship's surgeon. He bought them from a "merchant and druggist" named Eliakim Morse, whose store was located at No. 6, Dock Square in Salem. Any relation?
Hope this helps a little. Interesting - and relatively well-documented - topic.