Well the 570's line out is pretty good. It has enough of the basic tonal elements of what a CDP should minimally produce. You're just missing out on soundstaging, bass weight (particularly noticeable when I switch immediately from the 570 to 9000ES), transparency, airiness, etc, stuff you probably won't be able to seriously get without spending $500+.
If you're lacking treble bite, I don't think a source upgrade is going to give it to you. You might want to seriously consider changing your headphone. Changing your headphone is much more likely to give you the treble you want in much more audible amounts, than if you messed around with the source or cables. What you're asking for here is a tonal improvement, and IMO and experience, nothing gives more tonal improvement in an audio chain than the output end. And besides, the HD600s are arguably one of the smoother headphones out there, particularly in the treble. That alone makes me strongly suspect you should go out and look at another headphone, particularly the HD-590 if you want to stay within Team Sennheiser.