Ray
That version of the President is a little bit odd... I think Mr. Wilkins and his young protege may have used Chappelle's line drawing of the President as a reference and somehow confused the lines indicating the gun deck level with a representation of the gun stripe.
If it were me, I'd do a few simple things to the 1/96 kit to skew it towards the President:
1. Scrape off the CONSTITUTION name on the stern (obvious)
2. Replace the curved main fife rail with something more conventional/straight
3. Ditch the spider rail on the mizzen and put "normal" fife railing around the mizzen
4. Ditch the Trysail mast
5. Replace the double dolphin striker with a single
6. No white stripe... Perhaps yellow ochre above the wales.
7. Scrape off the Dragon on the trailboard.
8. Add a figurehead to represent George Washington (or possibly John Adams)
The "Don't Tread On Me" flag would not be accurate for any period of her existence.
The armament would be similar to what is represented in the kit (32 24-pdrs on gundeck, 22 Carronades (42 pdrs - a bit heavier than Constitution's 32 pdr, but very similar), and one 18 pdr chase gun.
The rigging was lighter and seemed to assist in her noted sailing qualities. Lt. Izard served on both ships and offered this assessment on the eve of war:
“This Ship [President] differs very much from the Constitution both in her Sailing and Rigging, and also her Accommodations; for she sails much better, and is much lighter rigged – Her Birth [sic] Deck is superior as also her Cabin, Ward-Room & Steerage all of which have the convenience of Air Ports- her Gun Deck and Fore-Castle are better; but her Quarter-Deck in my opinion is not as large – her Cockpit and Store Rooms are far superior to the Constitutions – The Master’s Boswain’s, Gunner’s, and Carpenter’s Store Rooms are forward on the Birth-Deck- her Lower Topsail, Top Gallent and Royal Yards are much lighter, than the Constitution’s; her Standing Rigging is smaller; but the stuff is much inferior; her running rigging is in some respects smaller but very disproportioned; and leads very irregular, but I believe the Comre. intends having it altered: the Eyes of her Standing Rigging are very large; and all of the Rigging is obliged to be kept very slack; for the least alteration in setting it up, would eventually destroy her sailing; but upon the whole I am very much pleased with this Ship and prefer her to the Constitution.” (Constitution Museum Log Lines blog)
Here is a link to a contemporary prisoner of war model of President in the Smithsonian collection:
http://americanhistory.si.edu/collections/search/object/nmah_1315846
Good luck with your build and please post some pictures!
Evan