I humbly submit the Ember as a recommendation. Yeah I know it's far under your budget, but it's what I have experience pairing the 560 with. I found it better at softening those sharp frequencies (I hope I'm thinking of the same problem areas as you) than the Asgard 2, which seemed like a pretty good amp already. Of course at your budget, you could start looking at the EC Black Widow. If I had your budget, I know I would.
This. In order of ascending budget: Project Ember, Cavalli Liquid Carbon (which I don't believe is sold out yet, but getting very close), EC Black Widow.
I listen to 90% electronic music, so a hard hitting kick drum is importent. Clearity and airness is also importent.