That was Zoe Palaelogina, better known as Sophia, which she changed her name to on marrying Ivan III as his second wife. She was a niece of Constantine XI by his brother Thomas who ruled in the Peloponnese. Her descent is believed entirely extinct, due in part to the murderous paranoia directed against his kin of her grandson Ivan IV .
Her last known descendant was her great-granddaughter Maria Vladimirovna of Staritsa, who died in 1610. She had two daughters by Magnus, nominal King of Livonia, a younger son of Christian III of Denmark, but they predeceased her, dying young and without issue. If you care to give her a son that survived and left issue instead, then a cadet branch springing from him might well have been thought suitable for the Greek throne a couple of centuries later. Complications with Danish history could be avoided by slotting his line in as Dukes of Schleswig-Holstein-Sonderburg-whatever (the last element tended to vary, especially in the junior line of Dukes which eventually did come to reign in Greece). This should be fairly easy to do as the real-world lines sprang from Magnus's younger brother Hans.
Complications with Russian history aren't inevitable. Although the line would be cognatic heirs of the Moscow Grand Princes and Tsars, such representation wasn't given too much weight in the Russia of the period, Boris Godunov for example becoming Tsar in despite of there being nobles with fairly recent female-line descents from the dynasty. Also the line would not be Orthodox, which was given weight, though they could of course convert, and finally they may well have been disinclined to venture themselves in the Russian maelstrom.
This doesn't seem to me to fulfil the terms of the challenge, which was for a specifically Byzantine rather than Danish via Russian line to be enthroned in Athens. However they would attain the Greek crown at least in part due to Byzantine ancestry. The actual George I of the Hellenes of course had some, but it would be impossible I would think to find anyone of royal blood at the time who didn't, and for some centuries before, all very remote descents though. The replacement line actually would, or to be more precise could depending on the exact changes made, have a specific representation of the last and longest-reigning Byzantine dynasty.