The Sextetts have a 200 mW power handling rating, their published effeciency 94db? I think is probably a little optimistic.
So working with the 200 mw, that is 11Vrms voltage from the amp. Most any headphone amp I have found is full of distortion at anywhere close the 11 Vrms. Compared to a speaker amp to reach 11vrms across a 4 ohm speaker a 15W amp is required, now the 600 ohm sextetts don't need as much current as the 15W 4 ohm speakers. But no speaker amp less than true 15W rms power will drive the sextetts to full power.
Now throw distortion into the mix, a speaker amp running full blast with 15 Vrms output (15W in speaker terms) is most likely not in a good spot for thd.
I can really understand how folks are reporting good results with 50W+ speaker terminals for the Sextett's. There really aren't any amp designs out there that have low distortion 11 Vrms 200mW output (only 18 mw), but you can see why it takes a 50W speaker amp to have reasonable distortion with the 600 ohm load.
Even tube amps which are supposed to be better for high voltage high ohm loads struggle because the output tube has to swing sp many volts before the step-down output transformer.
Has anyone found a reasonable amp that can deliver 10-11 V rms of clean power?