The question of human exceptionalism reminds me of something Kierkegaard wrote about freedom: Freedom is never possible; to the extent that it is, it is actual.
What he means is that the creature who wonders if he is free, is already free, for the act of wondering about freedom is itself an act of freedom. Unfree beings like rocks, trees, dogs or great apes, are not puzzled by the philosophical question of freedom. But man wonders if he is free, and is therefore free.
I would extend Kierkegaard's remark to include exceptionalism. Exceptionalism is never possible; to the extent that it is, it is actual. A creature who wonders about his exceptionalism is already exceptional with respect to those creatures who never do, or can, wonder about their exceptionalism.