The Quickie has a very low power output for headphones, 1mW in stock form as opposed to 50mW for standard headphone amps. That's about 17dB difference. It is a preamp, not a headphone amp, after all!
For that reason, I would expect higher efficiency phones to work better with it. Ideally, you'd like to see 102dB/mW rated sensitivity, with 96dB a practical limit. Should be loud enough for "normal listening," whatever that is.
The best you can do with the stock power supply would be to revise the operating point for maximum power rather than voltage, and use a choke load in place of the resistor load. That could give you as much as 6dB of boost - not a lot but should be clearly audible. Now we're talking 90dB-96dB minimum sensitivity.
Beyond that, you could raise the voltage. For another 6dB you could double the number of batteries (which would double the current so they last half as long). This quadruples the cost of batteries, so I don't consider it optimal, it just shows the sort of compromises available.
Crack, being current-limited, makes the most power into 600 ohm phones - around 200mW, which is 6dB above the reference. Smack can easily make 50mW into 600 ohms, and around 200mW into phones in its target range (16-250 ohms).
