I even asked you for 'evidence' to show artificially improving resolution via distortion

Great, I must have missed this part. I'm convinced that a subtle reverb can do it.
I like to listen with slight reverb by the way, so it's not just "regurgitated objectivist speech".

I dunno.  I can get used to a bass heavy phone over time due to acoustic reflex.  It makes bass heavy stuff sound neutral and everything else sounds bass light as a result.  It can go the other way too to an extent w/ bass light gear.  I don't think treble can be compensated for the same way biologically apart from using deafness.  Ears/brain also experience fatigue making distinct subtleties indistinct/blurred bringing most well performing gear closer to each other.  I think this one of many huge reason many listening tests end up w/ 50/50 results.  People's ears and brains just get overwhelmed from the prolonged switching and they biologically and psychologically shut down.  There are other big reasons as well.

IME overall balance is pretty easy to get used to.  Peaks are probably a lot harder to get used to.  Sharp ringing in an offensive range is probably close to impossible to get used to if it bothers you in the first place.  Probably the sharper and more abrupt the anomaly is the harder it would be to get used to.

At least if you've consciously noticed it in the first place.  If you never notice something in the first it can change rather drastically no matter how 'obvious' or straightforward it might appear.

If you can show me a paper or research showing how adding distortion increases perceived or actual detail and separation from a pluck of a double bass, strings on a Cello, smacking and parsing of lips, the sensation of air originating from the throat and not lips to the natural decay and ringing of a cymbal let me know.  I'm not talking about fake detail either that results from attenuating one side of the FR balance like say a Shure 1840/1440 does by cancelling out 1/3rd of the spectrum to better hear the rest.  I'm talking from 20 to 20. 

It's nothing as blatant as that.  It's just a little bit of extra second harmonic in the right place can sound like harmonics that actually belong there.

I have an idea for a listening test that could be done to see if an amp is adding or subtracting something from the signal.

Take an amp you like, such as the S7 or BA, and wire it's output in parallel with a pair of headphones and the input of an amp that measures flat, has minimal distortion, very low Zout, etc like the O2.  Then listen to the output of the second amp with another pair of the same model of headphone that is in parallel with its input. 

If the second amp fed with that input sounds the same as the first amp by itself then the second amp must be transparent to it input.  If the second amp doesn't sound the same then it must adding/subtracting something on its own.  If they sound different by themselves when fed with the same source and the second amp is transparent to its input then the first amp must not be.

That not a perfect protocol (even if it's done blind) but I think adding the second pair of 'phones in parallel would get close enough to simulating the load on the first amp when used normally considering what it's parallel with should be pretty high impedance and not reactive at audio frequencies.  The O2's Zin is 10K by default which would bring the HD800's nominal impedance down by about 3%.  Probably not audible.  Swappi ng the O2's input resistors for 100k would make only .03% lower.

I wanted to like the O2 so I could do a firesale and make my money back but stuff in my music just disappeared.

Grass is always greener huh?  I wish all that stuff was true.  Especially the crazy stuff.  Not that we're taking about it specifically, but I wish that different cables actually did make things sound better.  Easiest upgrade ever, especially if you're not afraid of DIY.  I think it would be nice if it was that easy to get better sound.

Amps are more expensive but it still holds.  From my perspective I'm limited by the headphones the someone else has already made and there's not much I can do about it.  I can DIY an amp arbitrary complexity since it's pretty much just following someone's plan and arranging the parts in the right manner.  I could even design it myself with enough trial and error.

I don't think I could do that with headphones.  I can mod existing ones, but making a new transducer from scratch (At least a non-'stat.  Those are actually not to hard to DIY with passable results though you probably rival Stax.) takes either manual dexterity or machinery that I don't (and likely never will) posses.

DACs aren't nearly as DIY friendly but it would probably be good trade for the rest of the package if I thought I needed something beyond my ODAC or Focusrite Scarlett 2i2.

To better answer your question I guess I could offer this experience/analysis.  I can hear the transparency of the ODAC using my less better measuring amps better than using the O2.  The O2 definitely gets in the ODACs way pretty obviously.  It's not unlike listening to a speaker w/ the grills on versus off.  It becomes pretty obvious when you hear things just get out of the way and know what to listen for.  I have a few theories about why the O2 sounds the way it does and where to look for fixes as I'm sure others probably know as well.  At least it's not a Leben and performs well for the price.   

I don't often bother (because I don't really think that uncontrolled personal experience is reliable when trying to examine such small differences) but I can relate my own experiences.  They're pretty much the opposite of yours in regards to amps and DACs.  When trying different models I usually either don't hear any obvious difference or hear something that's obviously wrong.

Could I be a tin ear or something?  Maybe.  I manage to pick up on subtler details of headphones that a lot of other people seem to miss.  Things that other people, like you purrin, and RD can hear.  They also tend to show up on the right measurements so they probably really are there.  If I can do that then I can't be all that bad.

I'd be interested in your theories about the O2 though...

I can get used to certain things.  I can get used to errors of omission much more easily than errors of commission (to use Purrin's terms).  For example, I could live with the HD650 or LCD-3 much more easily than a Grado or Ultrasone.  I also can get used to mild bass emphasis better than bass rolloff or upward tilting FR.  If I could get used to the K701 it would take a long time.  If it's all I had, maybe I could live with it sure, but it would sound thin and basslite for a ling time.  Same with the stock HD800 on the amps I've heard it on.  But more than any of that, I could never get used to resonances.  That's what sucked me into this hobby, they've always bothered me and always will till my ears stop working.  Cursed.

I suppose we all have a level and certain particulars that we can get used to, and then below that another level we could live with. 

But most headphones are way beyond the level that my brain can compensate for. 

Take an amp you like, such as the S7 or BA, and wire it's output in parallel with a pair of headphones and the input of an amp that measures flat, has minimal distortion, very low Zout, etc like the O2.  Then listen to the output of the second amp with another pair of the same model of headphone that is in parallel with its input. 

If the second amp fed with that input sounds the same as the first amp by itself then the second amp must be transparent to it input. 

I tried to represent what you are saying.



Both headphone should sound same, if the amp2 is truly transparent, if I've correctly  understood your  experiment.