Generally speaking, the greater step-down ratio to power such headphones will diminish the output power of the Quickie to the point where it is no longer very useful as a headphone amp.
If you can find a pair of AKG K-240M's instead of the other K-240 models, you'll get decent output from the converted Quickie, but the design was never intended to be a studio grade headphone amp (the SEX amp or the Mainline would perform far better).
-PB