I'm a kpop fan myself along with jpop and anime music i do most of my listening nowdays with my lcd 2 2016 which is perfect it's smooth sounding great for long listening sessions, forgiving & planar bass. Though female vocals do a habit for feeling a bit distance, but it's not something i really notice nor does it really annoy me unless i switch my headphones for something else.
I might advise against the hd 800 not sure about the hd800s but the hd 800 would be unforgiven to kpop and jpop it would be far to revealing of the badly recorded stuff one such song is 9muse dolls brought it from itune oh boy does it sound badly mixed even with my lcd 2 i feel like i'm being tested, i imagine the hd 800 would be a dagger in your ears The hd 800 is also lean in the bass area which is a bother to some people.
I have owned stax 2170 which i have listen to kpop and gamed with them, they are a little less smooth than the hd650 in the treble area. they do not lack in midbass but in the sub bass which did bother me time to time. The 2170 is also lean sounding which bothered me quite a bit for gaming the imaging was great however it felt a bit weird how things were strongly hard panned left and right, also during a game called killing floor 2 where i normally play on a custom server people would shoot and fire rockets, everywhere the stax kind off was overwhelmed and sounded too diffused, the same can be said about dynamic headphones. My lcd 2 managed to keep up and give me a sense of direction of where everyone was while at the same time shooting and firing rockets, even though the lcd 2 has a funky imaging ability.
I would look towards planar headphones if i were you. One headphones comes into mind would be the Edition XV2 it's very amp friendly so you don't need a top tier amp, has a big soundstage with good imaging for gaming.