Nietzsche's Eternal Recurrence was no mere thought experiment

Nietzsche's eternal recurrence is a popular topic in online forum discussions.  My book, The Illusion of Will, Self, and Time:  William James's Reluctant Guide to Enlightenment, culminates with Nietzsche's "ideal of the most high spirited, alive, and world affirming human being."  One endnote seems relevant to the frequently raised notion that Nietzsche was not fully committed to eternal recurrence:

Nietzsche’s passionate promotion of eternal recurrence as a reality, rather than merely a doctrine he had been familiar with and written about as a Greek scholar, came to him suddenly during a walk in the woods, as he approached “a powerful pyramidal rock” (Nietzsche, 1908, 295). The original mystical insight of this ecstatic vision supersedes the implausible physics he later tried to supplement it with: finite matter rearranging itself in infinite time into perpetually recurring exact replicas (see Nehamas, 1985, 144–145); see also, Kaufmann: Nietzsche’s “reasons for not publishing a proof [based on physics] presumably included his own sense that his efforts were inadequate” (1950, 327).  For such added-on physics were not “presuppositions that would have to be true if it were true” (Nietzsche, 1901, 545; emphasis added). The only presupposition of physics “that would have to be true” is what Bohm identified as physics’ real fact: an “order of succession” (Bohm, 1992, 233). The physics that does support eternal recurrence, special relativity, emerged five years after Nietzsche’s death [see Frassen (1962) contra Capek (1960)]. Attempts to construe Nietzsche’s “highest formula of affirmation” as a “thought-experiment” (Arendt), a “pretend” game (Sartre) (Lukacher, 1998, for both, 117), or, most recently, a “grand fiction” (Panaïoti, 2013, 128) run counter to “the strong emotion of the discovery” that left him “bathed in tears” for a long time (Halevy, 1911, 231). His beloved companion Lou Andreas-Salomé’s account of how he experienced it confirms as much: “To me the hours are unforgettable in which he first confided it to me, as a secret, as something he unspeakably dreaded to see verified . . . : only with a soft voice and with all signs of the deepest horror did he speak of it. And in fact he suffered so deeply from life that the certainty of the eternal recurrence of life had to entail something ghastly for him” (Lou Andreas-Salomé in Löwith, 1997, 197–198). These are not the expressions of experiment, pretend, or fiction.