Dear Matjet,
Re your inquiry about headphone amps: Stax headphones are electrostatic type so you need a special amplifier for them. I use an SRM727A with my Omega 2 (SR-007A). It's expensive on its own (around 1000USD) but peanuts compared to a source like the K01 and especially relative to proper amplification cost to make a good set of loudspeakers sing.
As to what you can achieve with a good headphone system: a lot! Personally, I have moved away from loudspeakers over 10 years ago and never looked back. The resolution and finesse of Stax electrostats is very hard to beat with loudspeaker based system, even in the stratospheric high end region... I had the privilege to listen to Stax's new flagship prototype (codenamed C32) and, imo, it sets a new standard for headphone based sound reproduction.
This Stax headphones have such resolution that a poor quality source is absolutely no go. On the other hand, unlike many loudspeaker systems, this extreme resolution does not make poor recordings unlistenable. It scales up with the source and recording but never sounds brittle or shrill unless you really feed it with garbage.
The bass is of course missing the chest impact of loudspeaker system but it is so clean and tight and goes very low so, personally, I have totally gotten used to this. It should be a nice experience with the K-01, given Esoteric's fame for solid low end reproduction.
Finally, for imaging, against some learning process is in order to reconstruct a plausible soundstage from headphone. But once you can achieve this, there are again very very few loudspeaker setups that will have such accurate 3D placement of instruments like Stax earspeakers (in particular the C32 which throws a wide and deep soundstage while maintaining perfect instrument placement). Again here, I can't wait to see how it will scale with the K-01!
Sorry for the long reply, headphone addict here ;) If you want to know more: www.head-fi.org...
arnaud.