Don't get hung up on just circum-aural phones though such are often used by better heeled headphonophiles. Most people use earbuds. On ear or in ear or near ear clip on phones with cell phones for a source. So as well as testing some headphone amps, and dedicated music players, test the output of popular phones. Iphones, Galaxies etc. plus some tablets. Oh, and definitely get some of the Etymotics.
Maybe after trying a few representative headphone amps for a baseline, you'll have something like the budget DAC thread. Phones or cheap players that compete with expensive rigs. I also think some low priced prosumer recording gear will have surprisingly good headphone amps for surprisingly little money with lots of capability thrown in for nothing.
Much like some exotic speakers, headphones and headphone amps create something of a vicious circle. Exotic unreasonably hard to drive quality headphones create a need for super duty amps which fuel the market for energy guzzling exotic headphones. Your Stax needing something like a real power amp are an old niche example. Though Koss preceded them (those Koss ESP phones were sweeter sounding than the Stax though).
I often find myself preferring my Soundsport earbuds from Bose, compared to my Sennheiser 598s. I get a strange and locked-in feeling from most over-ear headphones. Doesn't feel natural. The Soundsports, on the other hand, let in some external sounds, and in a way that feels much more natural. The only headphones I've tried so far which didnt make feel locked-in were the Hifiman Edition X V2. Felt open and natural, and played extremely well. Can be driven by a phone also. When I get the funds, I will probably buy a pair of those together with that thingy which recreates the HRTF and provides the feeling of listening to speakers in a room.
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