Made a simple booster for the headphone output & the myth was busted. No, you can't amplify the headphone output. It's much too noisy. The microphone "playback" is at microphone level when amixer says it's 100%. Amixer still scales it when it's below 100%. It needs 100x gain from the booster to be minimally audible for a middle aged, flat broke lion.
The noise was what killed it. Disconnected the booster input & most of the noise went away, so it's partially the virtual ground & partially the line output. Haven't tested it, but if all inputs are constant, a high speed op-amp shouldn't amplify power supply noise.
The final way to save the Generalpro is to wack the self monitoring headset board in. Its only downside is having to use a pot to adjust monitoring volume instead of the web app. For the advantage it gives beyond a phone, the generalpro is proving much less worth it than the full 24 bit ADC. It might even be worth stepping the 24 bitter back up to 96khz. Any kind of 96khz audio would require buying a TOSLINK DAC for the amplifier. It's probably not worth hacking that, even though the parts are around.