keep in mind that is power that's important, not current...
In an ideal amplifier, where the amp can supply infinite amounts of current/voltage, and there is no Iq, then impedence has absolutely no effect on battery life. Low Z phones will draw lots of current and have very little voltage drop, vice versa for high-Z phones... The power drawn is the same regardless of the headphone's impedence... Its SENSITIVITY, in dB@1mW that determines how much power is needed
If you want to factor in the amp's quiescent current, then low-Z headphones actually become more efficient than high-z phones. As you said, a 600ohm headphone will draw less current than the amp's Iq. As a result, the power that is lost due to Iq is very high. If a low Z headphone was used, then a much larger current would be drawn, and Iq will make up a much smaller fraction of the overall power draw. And, in addition, Iq usually goes up with higher voltages, which makes high-z headphones even less efficient...
The reason that 9V's suck for high current amps is because they have very low power densities. THey hold much less power/unit of volume than AA's...
BTW, you're crazy... how the hell do you get 150mA out of a portable amp!!! I'm lucky to draw 50mA out of 4 class A opamps! are you using class A discretes or somthing?