Don't know if it might help somebody, but my HK6 were picky about the sources (probably also about tips, but since I went directly to the Spiral Dots, I did not experience any variations), sounding way better balanced from the Shanling M3s than from the Sony 300a. I liked how they sounded on the Shanling M3s from the very beginning, so I put them on burn in there. I know this may sound a bit crazy, but my personal experience with burn in is that things at the very beginning give a good inkling of how they will sound towards the end of the burn in. Then things fluctuate, usually sounding worse, and then get to a point at which they are stable. With the HK6, after the first day, and even after around 200 hours, I did not like how they sounded, even on the M3s. They did sound a bit muddy, and congested (and my memory said they did not sound that way, at the beginning). So I left them on burn in some more. After 350 hours they are way better, no muddiness that I can hear. And memory (which can be very tricky, though, since around 2 weeks passed) tells me they sound better than at the very beginning.
So, to those who have them and don't like the current sound, my advice would be to really cook them in, before throwing the towel on them
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On a different, more cautionary, note, I'll share that I was an idiot, and quite likely ruined my M3s yesterday... I had trouble ejecting the micro SD card, but finally managed. Then, when I went to put another one back in, SOMEHOW, the new one managed to get inserted, through the (VERY narrow) slot in the chassis, not in its proper place (the thing that clicks and holds the SD card when you push it in - its "sled"?), but probably below it, and it's impossible to fish it out (tried tweezers from the swiss army knife - slot is too narrow to allow them to open and grab, once inside - and tweaking with a needle point trying to coax it out). So now I have a brick without music, and I'm out a 256GB micro SD. I would have thought that that was (or should have been) impossible.....