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[Formendacil]

Found the Letters Bêth and I referred to. First, mine, regarding Tolkien's use of Byzantium for Gondor:

But in the north Arnor dwindles, is broken into petty princedoms, and finally vanishes. The remnant of the Númenóreans becomes a hidden wandering Folk, and though their true line of Kings of Isildur's heirs never fails this is known only in the House of Elrond. In the south Gondor rises to a peak of power, almost reflecting Númenor, and then fades slowly to decayed Middle Age, a kind of proud, venerable, but increasingly impotent Byzantium. The watch upon Mordor is relaxed. The pressure of the Easterlings and Southrons increases. The line of Kings fails, and the last city of Gondor, Minas Tirith ('Tower of Vigilance'), is ruled by hereditary Stewards. The Horsemen of the North, the Rohirrim or Riders of Rohan, taken into perpetual alliance, settle in the now unpeopled green plains that were once the northern pan of the realm of Gondor. On the great primeval forest. Greenwood the Great, east of the upper waters of the Great River, a shadow falls, and grows, and it becomes Mirkwood. The Wise discover that it proceeds from a Sorcerer ('The Necromancer' of The Hobbit) who has a secret castle in the south of the Great Wood.

--Emphasis mine, taken from Letter 131, to Milton Waldman. Some copies of the Silmarillion have this letter, in part or in whole (not sure which) as a foreward of sorts.

Bêth's reference:

Thank you very much for your letter.... It came while I was away, in Gondor (sc. Venice), as a change from the North Kingdom, or I would have answered before.

Letter 168, to Richard Jeffery. It's possible Bêth has another letter in mind, but this was the only one I found on a cursory look through.