You can still do some things...
You can run the signal through a hub chip to try and clean it up...
You can feed that hub chip with a fancy clock for hopefully less jitter...
Use a better power supply...
...but you just can't break the ground. No isolation.
You can use the sensitivity rating on your headphones to guess-timate the voltage required to drive them to a reasonable
level and use their impedance to figure out the rough current.
You can get the quiescent current for the op amps from the data sheets.
Other than having to charge up that big a55 cap bank, it's just a three channel CMoy.I think the 100mA should at least get it running. Just add up the quiescent currentfor the three channels and add in how much current you think you may draw under load.
The Panasonic in the power supply and ELNA Silmic II in the signal chain is how I would go too.
Nichicon also makes some good power supply and signal chain caps.
Look for something with good ripple current for the power supply.
Have you tried DigiKey and Mouser? They usually have a pretty good stock on a wide variety