Re: K712's do not translate: Whats better? DT880's?
I've been using the Hifiman HE-400i for a few months now. They're open back, but they're also planar magnetic, which means they don't have much of a bass roll off until you get down to 40 hz or so. They get compared a lot to the Sennheiser HD-600 in terms of being pretty neutral from top to bottom (though with the Hifiman having more bass). The Hifiman beat my Sennheiser HD 280s (which are my only closed headphones) in the bass department handily IMO. It's not any louder than they are, but it is so much clearer it more than justifies the slight loss in volume.
I think if you want to stick with headphones, you'll end up with the HD-600 eventually, or the HE-400i if you want to be a contrarian like me. They're both expensive ($300-$500 US, depending on if you catch them on sale or something, I've seen them dip into the $250 range, but that never lasts) and priced pretty near each other, so I'd compare those two and see what you think will work best for you. Either one will be fine through your O2.
You could also consider the older HE-400 from Hifiman, which you might have to pick up used, but are much cheaper (around $200?) these days. They had a bit more bass, but were not as 'clear' as the newer model.