Sounds like you are saying that the HE560 is slightly dark. Not as dark as the HE500, but slightly dark. Is this correct?
What amps have you tried with the HE560? I am considering the Emo Mini, Schiit Mjolnir, and Audio-GD NFB-6.
If the HE560 is slightly dark, the Mjolnir might be a good match. What do you think?
Not quite, it's not slightly dark, some might even feel it is slightly bright. That is treble behaviour, I'm talking midrange behaviour.
HE560s would work best with neutral ~ warmish-neutral upstream, I think.