You should compare AD8397 to LM4562, AD8058, ADA4899-1, discrete buffers or anything else with articulate treble with HiQ full size cans and then tell me it's not shrill. If you compare it to OPA2134, OPA2107, AD823, AD8066, AD8620 etc you wouldn't find it shrill, because they all are. If it weren't shrill, it would be the perfect opamp, and we would have had the best amp in the world in our pockets, and there would be no market for fancy amps at 10 or 20 times the cost. If it had no flaws, why would anyone look for anything better at all.
I only mentioned the ER6i because if the AMP is shrill, the ER6i don't like them. My Tomahawk makes the ER6i worse, and I don't hear anyone esle call that one shrill. I do know shrill - I will not for for Shrillery Clinton for example.