I actually didn't find the K712's all that accurate. Instrument separation was great, but actual imaging was sub par, as it was applied in games at least. It's strength was music, though I find the treble fatiguing, even more so as it applied to gun shot effects. They worked well for movies, if bass slam isn't a requirement.
I think the X2 offer a lot of the capabilities you need, but I found them uncomfortable after several hours of use. I'd recommend more to the 558/598 side of the debate for comfort and gaming, but they lack the bass to make some movies really engaging. One problem you might run into is whether you can drive the headphones using something like the MixAmp. I guess I could test some of these for you, in that regard. I know the X2, 558/598 and R70 wouldn't have much issue though.
The R70x is comfy, and non-offending, in that the bass isn't overly in the face, and treble isn't harsh, partially because both are rolled off. Which is great for long-term listening, but bad if you want to be engaged by audio. It's driven sufficiently from my PC, MixAmp Pro, but not quite efficient enough for my phone to get decent audio out of.
The 400i is great, but needs an amp. It's my current all-rounder pick, but again, needs an amp. The 400s is more efficient, but sounds a bit more muddy without a bright amp to help clean it up. Both would work well for your intended use. The sound stage is smaller than the K712, but I find it images more accurately, at least in games.
I haven't used the Shure's so I can't comment on them.
But to get your homebrew headset going with a PS4, you'll need a MixAmp or something similar at the least. It has a built-in amp, and anemic as it is, it's good enough to drive about half the headphones on your list. The DAC is built into the MixAmp, so there's that.