I'll third the recco for Lake People/Violectric amps (I've owned the G109 & V200.. used it with IEMs, dynamics, and planars.. the sound was terrific.. especially with planars). I've heard nothing but good things about the Asgard 2 (and I tend to love Schiit's stuff).. it probably offers the best value out of the solid state option in play here. I can't comment on how it sounds since I haven't heard it, but many people's opinions who I trust have said the A2 works great with the HD600 (and most planars, as well).
That being said, I settled on the Bottlehead Crack (w/ speedball) for my HD600... and it's a match made in heaven. From what I understand, the 'regular' Crack (w/o speedball) has a more stereotypical "tube" sound ("warm, syrupy, romantic, etc.").. the speedball tightens up the sound, improves resolution, lowers the noise floot, and takes the Crack in a decidedly 'solid state' direction, sonically. I've had the Crack+SB for quite some time (and own/have owned a number of solid state amps in that time) and tend to agree with that assessment. The thing is, The SB'ed Crack doesn't sound 'sterile, cold, or clinical' in that way some solid state amps tend to sound (to my ears). You still get the 'tube goodness' (see: pleasing distortion), but the sound isn't slow or overly warm. What I liked most about the Crack is how it presents the HD600's bass (tight, punchy, fast, and better extended than I expected) and how it improves soundstage depth (over many of the solid state amps I heard the HD600 with). There's obviously a lot of great options out there for the HD600.. but after hearing/using the Crack with the HD600 for a number of months, I've got no desire to chase another amp for it. IMO, it's worthy of being an 'end game' headphone rig.
I think the just released Schiit Vali is another terrific option if you want to go the tube route but don't want to mess with 'rolling' or DIY.