I'd wait to hear some reviews on the Asgard 2. If you follow the thread, there have been lots of kinks w/ this new release. But it could be a great amp, better than the first one, which I thought was kind of congested and too warm w/ the HD600, though having plenty of juice. Other love the combo.
I've owned both the HD600 and HD650 and own both currently. I think there are lots of options under the $300 mark with no clear winner. The E09K is really good with the HD600. The O2 is also quite adequate, though at this point I prefer the E09k over the O2. I thought the Schiit Magni was too bright and thin with the HD600, though some have liked the combo. I've got a Headamp Micro coming now aftering reading positive reviews for the classic. It's on sale from headroom now for $249. I'll let you know how it goes.
I think the best budget amp I've heard w/ the HD650 (though I didn't have the HD600 at the time) is the Yulong A800. I'm one of the few users on the forums who have had one and I regret selling it, though it was the right choice at the time; you won't find much written on it. You can pick it up on ebay or from grant fidelity for $179. Slightly warm sound w/ incredible power and great dynamics. I'm going to rebuy one in the next couple weeks and write a proper review. I don't think you can go wrong trying it. It would be my first choice, I think.
If you do DIY stuff, everyone will recommend the Bottlehead Crack. I wish I did DIY. I'd love to hear the Crack.