on a strictly technical basis I would recommend dropping the dual buffers to just 1 per output, with the HD580’s 300 Ohm load the extra output buffers are simply silly, you only need 30 mA to swing 9 V on the HD580, the BUF634 can do 250 mA apiece
even more unsound is the use of 2 buffers on each output when the active ground has to soak up both channel's current and you're being offered only 1 buffer in this position - the ground channel really deserves as many buffers as the sum of the output channels, but for the HD580’s 2 x 250 mA ground buffers would be overkill
The 300 Ohm headphone impedance means you want every last Volt of output swing, I would look for the 9.6 V rechargeable "9 V" battery for this application (Maha?) - if you pay no attention you could end up with a 6 cell, 7.2 V "9 V" rechargeable, or the 8.4 V ones
by dropping the unnecessary paralleled buffers you make up somewhat for the lower mAHr of the higher Voltage batteries
http://www.thomas-distributing.com/mh-96v170.htm
a downside of the AD8610 is the +/- 13 Vmax supply rating, with the 300 Ohm Senns you want all the voltage swing possible and the 8610’s reliability would be iffy with a 24 V unregulated wall wart supply
The AD823 is very well regarded, cheaper than either previously mentioned op amp and swings rail-rail on the output with up to +/- 18 V supplies