Working through the NJM4556 chip maximum dissipation numbers, it appears that a +/- 18V rail modification on the O2 would support not only 600 ohm headphones, but impedances down to 250 ohms. The K240DFs that have been mentioned in the Head-Fi thread are 600 ohm and 200mW headphones. The 153mW maximum of the 18V version would be a good match, probably better than the 88mW maximum into 600R of the standard 12V O2 version.
The NJM4556 maximum dissipation with the +/-18V rails and the 600 ohm headphone load is the maximum total (RMS) input power to the chip minus the maximum load power: (17.6V)(16mA) - 156mW = 125.6mW. That is substantially under both the NJM4556 rated dissipation of 700mW and an ambient-derated guess of 500mW, so dissipation isn't a problem. With a 250 ohm headphone load the maximum NJM4556 dissipation goes up to around 307mW, still in bounds.
I've attached a BOM with the changes to make the O2 work with 18V rails for 250R - 600R headphones. Best to wait until RocketScientist weighs in before ordering anything though!
I could easily be missing something about the 18V modification. But from what I can see in the simulation it would work just fine as long as
only 250 ohm headphones or above are used and nothing lower impedance. Lower impedance cans could result in excess power dissipation in the output chips and likely too much current out to the cans.
Even at 250 ohms that is a maximum of 376mW to the cans with a maximum source and the volume all the way up, likely more power than they could handle. With 600 ohm headphones though that most likely isn't and issue.