You can take my advice or leave it, especially in light of many of the other suggestions you've seen, but I'd say you've got the right idea here: IMO, the differences you're going to see with different equipment are often overblown once you've reached the point where you're properly driving the headphone in the first place. In your case, your mixer is most likely the only one doing this for you. I actually have an old Behringer mixer myself with a surprisingly decent headphone amp section that I used for many years to power my headphones (before upgrading to different equipment), and my HD 600 sounds like it should when powered by it. I'd say it's likely what you're getting out of your mixer is representative of the fundamental level of sound and performance you can expect from a properly-amped HD 600.
Now if you want to dial in your sound and get that last little bit of performance, there's nothing wrong with going for a nice amp and/or DAC (notice I say nothing about cables
). Just don't expect a complete transformation; what you get at the end is still going to sound like an HD 600, for better or worse.
Not to go too off topic in the HD 600 thread, but if you want more shimmer in your treble and a bit more low end extension, have you looked at the DT880? As one of this headphone's longest running exponents on this site (almost six years experience with my pair), I can say it definitely has more treble presence than the HD 600, while retaining an overall similar balance (i.e. it has less upper midrange presence and better bass extension, resulting in a very slight V-shape as opposed to the HD 600's slight warm tilt--both can be considered interpretations of neutral). Between the two these days I lean more toward the HD 600 as my favorite, but I would say the DT880 is right up there in technical ability--maybe just slightly less resolving and coherent overall, and a touch splashy in the lower treble in direct comparison to the HD 600. I realize you've already got an HD 650 on the way, so I can understand if you're not particularly enthusiastic about buying
another headphone on top of everything else, but I just thought I'd throw this suggestion out there as it seems relevant to where you say you're having trouble with the HD 600.