I can only play through headphones with my current situation. I play late at night in an apartment. No exceptions. I've been on a headphone trying spree the last couple of weeks, going through a Beyer DT770, Senhiesser HD280, Audio Technica ATH m50x, and m40x. All of them are the same result. Fizzy distorted tones and lifeless cleans.
I feel your pain. It should sound fabulous. I have a few questions. Have you compared the sound of the Kemper from its headphone output vs. through your interface? Are you running stereo? What interface are you using?