The HD600 was my first serious set of headphones, and I’ve always found it electrically modest but extremely noise and amp sensitive. I went down the balanced path in large part to control its hiss and high range scratchiness. I don’t bother with balanced for most of my other headphones.
Many chip amps do that, and they all sound about the same, and they usually generate glare to my ears.
Also consider the Class A RebelAmp. It’s my current default solid state amp, and I don’t care to upgrade. It’s available in green or black.