Ok, but your essay implies that he changed his mind about it —that his “later” thought overcame the earlier approach. If he kept returning to the “arc” language, then he was articulating a kind of whiggish moralism.

If it matters, I think that King is expressing an ambivalence within Christian thinking on history: between "apocalyptic" (redemption and hope breaks in from outside history) and "providential" (history is upheld and guided by a just God). It's not a contradiction, but it's a "tension".

Yes— my original draft was clearer on this at the expense of too many words, and they got cut in editing.