110% not designed for listening to music. DSP for music is pretty bad, not the worst out there but from being into HiFi for the past 20+ years, I can tell you that these are not the phones to buy if listening to music is a priority, or even a minority. Walk on by and get a decent set of phones. Even the HQ software says it all, all presets are for gaming, the "music" preset is a bluff, don't fall for it!
That's extremely odd. Did you contact Audeze and get the firmware update? Because there's definitely something wrong. You are the first person that I have seen say that they are bad for music. Reviews have complained about the controls, about the 3D preset when playing movies, about the Bluetooth only having stereo, about the mic quality and about how gimmicky head tracking is. That's the main complaints. I can understand that they might not sound as good as more expensive head phones but to say they are rubbish for music, can't be anything else only a faulty headset. While I might not have had much experience with headphones over the past few years, and I am no audiophile, but, I have been involved in hifi for as long as you have and have a really good setup for music at the moment and I can promise you this, the Mobius doesn't sound bad for music at all.
The most popular presets for music are Racing and Default. If you have the firmware upgrade people like the Warm preset too. Did you change the size of your head in the Audeze app? Also change the ambience to suit yourself. I find 25 to be the sweet spot.
Are you using the USB or the 3.5mm connection? If you are using the 3.5mm connection plugged into a sound card's headphone jack they don't sound that good. They will sound better using the line out. That's the only thing I can think of that might be as I tried them using the 3.5mm headphone jack in my creative Z and they didn't sound good at all.
So if you aren't using the USB connection, suggest you try it. If you are using the USB connection, there is actually one thing that might be causing the problem. You might not be plugging in the cable correctly into the headset. I have seen a few people report that this was their problem with the sound quality.
With the comparison with the K712, you are comparing an open back headphone with a closed back one. Next time you are listening to music, leave it on two channel and turn on 3D. This is how you increase the sound stage and imaging on the Mobius.
Love your setup by the way. Looks amazing!! I am well jealous of how neat and tidy it all looks. My desk is tragic lol.