I'm pretty sure the headphones you're thinking of are electrostatic and electret and not orthodynamic headphones. Orthodynamic headphones, while requiring more current than standard dynamic headphones, can still be run off most any amp with a decent enough power output. Here's my current rig for an example. It's being run off a standard portable amp (granted its the 627 MICRO, which is a really powerful single-ended portable amp for its size).
I always tought that orthodynamic headphones and electrostatic headphones were the same thing, just a different naming in the end of the day, are there any more accessible orthodyanic headphones?