With NFB taken at load end of the build-out resistor, it is still unstable with capacitance on VGND.
1K seems a high value. This would be fine if the load on VREF were several 100K bias resistors.
But you seem to want double-up. What is VREF expected to drive?? If the return from a headphone, 1K is larger than it needs to be. One 19-cent opamp can dump over 20mA. Batteries are usually low-voltage. 9V batt with 3V swing, 3V/20mA= 150 Ohms. Actually 100 Ohms may be fine.
Yes, you can use a quad opamp, even 47r for each, and get over 100mA VREF current.
However all this VREF current just heats the opamp and Rs. On battery, waste heat is bad battery life. When you reach this level of power, it may (and may not) make more sense to design the audio circuit as a bridge, double your available output swing. (The specific case of 3-wire stereo headphones is difficult.)