Well, just took a look at my copy of Articles
again. The Appendix tells us that Ra-ghorateii actually served 3 terms, and took over after the special election to replace Roth in 2288. So him being in office from 2289 - 2300 is correct.
Sulu being President is from IIRC The Return
, but that was the only place where it was claimed 3 presidential terms was unprecedented. That can't be the case if Ra-ghorateii served 3 terms, unless the lack of precedent means that there wasn't anyone who had won 3 standard elections in a row rather than 1 special election (even if for a mostly full term) and 2 follow up elections.
Also "unprecedented" was as of the time Sulu took office (2330s). Which means by the 2350s it might have become something of a de facto
term limit. So there's nothing preventing T'Pragh from serving till 2364.
OTOH, Amitra being a pandrilite, I have no idea what her species' average lifespan is like. If T'Pragh served 3 terms, it would mean she was a cabinet minister for 20 years. Which seems like a really long time to be a cabinet minister. (OTOH if she was the equivalent of the Secretary of State she might have thus wielded sufficient diplomatic leverage to actually push through the end of the Tzenkethi, Talarian and Cardassian conflicts).
Also she's still alive circa 2380...
Re the Tzenkethi War.
My timeline is definitely off.
Dr. Emmanueli thinks about not having spoken to her children in 15 years. She became estranged from her children because they believed she'd lied to them about dying. She was held by the Tzenkethi for 4 years, some of which was after the conflict ended. Which means the Tzenkethi War could have ended anywhere from 16 - 20 years prior to 2380. (The time when she was declared dead is described as "after the Armistice" though so it might be before a final peace treaty.)
At the same time, Sisko's experiences under Leyton on Okinawa
took place sometime after 2360 from the events if Catalyst of Sorrows
are to be believed.
A Singular Destiny
says Sonek Pran wrote his monograph in 2351 and T'Pragh brought him to the Palais to discuss it at the time. Sonek also describes his service to the Federation government as having spanned 3 decades as of 2381. So it seems pretty clear T'Pragh was in office in the early 2350s. Moreover he also served as an adviser to Jaresh-Inyo and Amitra, as well as one more unnamed President (Esperanza notes 3 other presidents other than T'Pragh kept consulting Sonek and since Zife cold-shouldered him, there's someone other than our named presidents in there).
One fudge may be that Bacco describes there being multiple
wars with the Tzenkethi (meaning the Tzenkethi might have tried to attack the evil empire several times during T'Pragh Administration, but it was only during a successor admin where Starfleet decided enough was enough). But I will have to revise and resubmit later on this chapter.