So in my case there's no workaround using the existing components or amplifier that I have? I am limited to a Li-Po battery which has 4.2V max. Do you know any headphone amplifier that is more compatible?You can't use any "Bridge-Amp" with only 3-Wires,
regardless of whether it's a Digital, or, Analog, Amplifier.
All Headphones that I know of only use 3-Wires.
If You want more Volume .............
You will need to supply more Voltage to ANY type of Amplifier that You want to use.
A simple and cheap "Dual-Op-Amp" will blow your ears off "if" You Power it with at least ~12-Volts,
and do it with extremely Low-Distortion, ( if You choose a high-quality Op-Amp ).