Yeah, that's essentially the CMoy amplifier. You replaced all the biasing drama with a virtual ground. Note a complete absence of capacitors in the signal path.
Which is perhaps an acceptable option, but I was mentally stuck in the realm of single supply AC coupled circuits, as suggested by the OP.
This circuit has DC coupled signal path, so potential disadvantages:
- DC offset of the source is passed to the load
- DC offset of the opamp too, at 9x gain
- in presence of DC offset, supply rails may get asymmetric due to high resistance of R3,R4
- if the two channels fail short to opposite rails, DC fault current flows through the two transducers in series
OTOH, the AC coupling of supply rails to ground saves transducers when only one channel faults or both fault to the same rail, which is surely a more likely scenario.
DC offset problems could be reduced by AC coupling between stages, like O2. Only a pair of small caps is required. This means the gain stage no longer gets to support the output stage with additional load current.
edit
Another (unrelated) disadvantage is less efficient use of the opamp's PSRR, compared to grounding the more sensitive supply.
There is also an advantage: any distortion of load coupling capacitor is removed from the signal path.
OP will have to decide which topology to choose. Last time I remember the topic of simple headphone amps, the OP was hell bent on AC coupling the load for the sake of safety/reliability and rejected all DC coupled split rail / dual rail suggestions.