The low end Stax tend to be bright and flamboyant, not what you'd call fatigue-free. I've yet to hear anything currently in production more relaxed than the Omega 2.
You need something that isn't bright, which leaves out most headphones right off the bat. So the only real choices at the high end level are the O2's and the LCD-2. The LCD-2 are really good, they have a calm treble, and they're not particularly forward sounding. I would recommend these if you have to have a normal headphone, as they are great in terms of value.
But if you want the ABSOLUTELY MOST fatigue free headphone that's readily available, I would really want to know if there's anything better than the O2's in this regard. The LCD-2's don't even come close, and it's because of a stat's unique effortless/ethereal presentation. Some will not like this because it lacks the impact/balls that one might enjoy experiencing, but that's exactly what you need if you want something fatigue-free.
The final nail in the coffin is it's forgiveness, when you have a (really)bad recording, the LCD-2's will fail to resolve the wall of sound that will inevitably ensue. The O2's do not give you a wall of sound, even if the bloody recording calls for it, that's how forgiving they are.
I'd buy the LCD-2 first and see if you like it, if you feel it still makes too much of a kick in the fuss, then think long and hard before buying the O2's, as they're pretty expensive. I've had them both at one point in time, simply to find the most forgiving/fatigue-free headphone.
The Sigma and the K1k might be more fatigue-free, with it's out of head projection, but too bad they're difficult to come across nowadays.