I understand the impulse to get a single solution for all your listening needs, but to be honest, that's going to mean compromising in some area or another. It may even mean an unsatisfying result for both music and gaming. The most tolerable compromise would be get the 2C and use EQ, something like Equalizer APO, that effects all system sound. Then, you can simply set up EQ profiles to dial in the perfect sound for each application. The 2C is an excellent candidate for that approach because the resolution, impact, and soundstage are excellent and for gaming you'd really just want to thin out the bass and fill in the lower treble dip a bit.
As a second headphone, the 560S is an outstanding choice for music, but I haven't ever gamed with it. I suspect that it would do well, but not exceptionally well. When gaming, I find the best approach is a headphone that has tight, even lean, bass that doesn't wash out details, wide soundstage, excellent imaging, and a generally clean, fast, detailed sound. My gold standard then is the HD800S. The 560S and HD800S have weirdly similar graphs (at least if you compare them on Crinacle's site), but in practice they are miles apart. The 560S has a much slower driver, resulting in more bass bloom and a more intimate presentation to the music. It feels somewhat closed in and struggles with layering/separation of sounds when things get hectic. In practice, that's going to mean more difficulty in separating distant gunfire from close gunfire or discerning between in front and to the left and behind and to the left. Now, obviously the $200 dollar 'phones don't do as well as the $1600 'phones, but I think there are other options for a cheap gameplay headphone. The one I think of immediately is the Philips SHP9500.
