I won't touch the balanced vs SE debate. I will say that the 650 responds and "scales" nicely with better amps and dac for that matter.
My opinion on the amps I've tried:
1. BH Crack with speedball 10/10 You just won't do any better in terms of pairing and getting the absolute best sound from the 650 or 600.
2. Schiit lyr 9/10 Drives the 650 nicely with good dynamics and the tubes give you the option to tweak the signature. If anything, the lyr seems a touch warm and will a bit of bottom end albeit just marginally. The lyr is tried and true and a safe bet.
3. Asgard 2 9/10 Not quite the same levels of dynamics as the lyr but more refined. Bass is tighter with slightly more texture. A bit more resolution on the top end. The A2 is a clean mostly neutral amp and it will work well if you're looking to "balance" the warmer nature of the 650.
4. Vali This is the little amp that could. Both dynamic and clean. Packs serious punch for such a small amp. Slightly warm but very close to neutral. Crazy good with a nice dac behind it. If you don't mind the microphonic issues during the warm up period, the Vali is hard to pass up at $120 8.5/10