well, if they want a dead language, why not Latin? (language of Rome - whose laws and building styles were emulated big-time by the Founders)
Greek just has too many problems....even the Helenophiles like Lord Byron bemoaned how the "heirs of Homer" had become inferior to the Turkish horde.
Latin remained the language of scholarship, including medicine, law and science, well into the twentieth century, so its choice would be far more likely than German or Greek. Besides, Latin is the root of so many other languages, including non-Romance ones via church influence.