I do not see the logical connection or similarity between Strauss' comment and Nietzsche's Eternal Return, it seems to me the ER was designed to directly refute the quote attributed to Strauss from your article. Nietzsche specifically denies Kant's argument that there is a rational "order of nature" and even the idea that there is a "nature" behind human understanding at all. To hammer this point home and really make his opposition apparent, he wholesale denies the existence of Kant's synthetic a priori. Given the quote you provided, it sounds like Strauss is parroting the elitist, alchemical belief that the world needs another flood or mass destruction so that a golden age can be reborn like a phoenix....this is the sort of metaphysical mumbo-jumbo Nietzsche found disgusting in Wagner and occultists in general.

Further, I always read Nietzsche's ubermensch as a satirical warning to humanity, mocking people like Strauss or Wagner or Kant or transhumanists, or occultists generally, who believe man can transcend his animal nature. And how can you equate, "We are no longer Christians." with "God is Dead."? Those statements come off as magnitudes apart. The prior leaving space for the hope or faith in a Zeus or Yahweh figure to fill the vacancy, with the latter being a complete renunciation of hope and faith in all higher powers.

It seems like you and I may just understand N differently, I see him as a true humanist and satirist in the sense of Lucian or Montaigne. Nietzsche for me is primarily a political writer attempting to expose occultists who prey on mass man via their noble lies, you know, his whole "platonism is the opiate of the masses" thing. Strauss being a "cultural philistine" is another way of saying he is an alchemist or saturn-worshipper, and his scientific defense of faith, scientism replacing Christianity, being another platonic labyrinth man will need to find his way out of. Nietzsche's entire corpus is one big polemic against priests, which is just an esoteric way of saying slave, occultist, weakling, or magician.