Another hopeful thought: we might escape being eaten for an unexpectedly long time because evolution is stupid. It might consistently program organic life to maximize for proxies of reproductive success like social status, long life, or ready access to food, rather than the ability to tile the universe with copies of itself.

This in no way implies humanity's safe forever; evolution would almost surely blunder into creating a copy-maximizing species eventually, by sheer random accident if nothing else. But humanity's window of safety might be millions or billions or trillions of years rather than millennia.