Epistemological certainty is a straw man: nobody's suggesting we reason our way through all this on anything other than the balance of probabilities (the nature of that balance being the point of disagreement.)

That's good.  Because many in the Obj camp have defined 'transparency=flat FR+low distortion'.  It's really not a straw man at all when there are those that fit the profile and regurgitate it.  It's a straw man for you, but not for others as they live and breathe it.

The 'potential implication' is largely your own. Besides, you cannot eliminate all the other factors that could cause you to hear differences, aside from the actual performance of the equipment, via experience, or anticipating the effect of such factors and consciously trying to guard yourself against them (seriously, your skill or experience as a listener doesn't render you even partially immune to non-auditory difference factors). Likewise, the arrival of some sort of minimal consensus within a small, or even a large, community is hardly proof of anything, regardless of how compelling it may seem as confirmation from the inside.

Nope, can't eliminate anything but you can compensate.  Various mechanisms for trying to eliminate biases can in fact introduce new problems even.  Expectation bias is also largely irrelevant when your subjective impressions end up being 180 degrees contrary to what you anticipated and happen to correlate w/ independent impressions of people you never spoke to.  The presence of expectation bias or bias does not delegitimize the significance of shared independent experiences.  The question should only be a matter of threshold/bright line standards of validation.  Whether one is looking for data or definitive 'proof'.  Even the word 'proof' is a loaded word.  The sort of proof some often seem keen on repeatedly espousing is anything but according to what I consider 'proof'.  'Proof' isn't even a word I would ever use wrt anything we do or have done here.  We have objective data and evidence that often correlates to subjective experience, there is no 'proof' here of anything.  Nothing here is established as a 'proof' and neither do any tests or conclusions supporting null hypotheses constitute any sort of 'proof'.  The fact that some would use that term while others like myself would not indicates an inherent distinction between our perspectives.  For some, seeking proof is a religious crusade using science and math as a God.  This is understandably inherently so by the intrinsic nature of humans seeking security, validation and certainty.  Most of us just want more data wherever it comes from as a matter of being more informed while others want to preach universal maxims to find comfort within their own ideals.  Not you of course. 

When it comes to amplifiers, the fragility of the impressions as evidence for anything is extreme, due to the combination of the small size of the differences and the opportunities for those differences to be caused by other factors, so even if you feel they are adequate surely using a testing protocol than can account for anything happening of electrical significance known to physics in the output of an amp/DAC to investigate them would be a good thing?

I didn't say subjective impressions are completely adequate in totality.  I said they a not irrelevant meaning they should not be discounted out of hand.  Many of us do use various testing protocols and continue to build and expand upon them as part of the entire review process.  While perhaps not definitive (whoever would be able to define what definitive would be) I'd say their value is greater than random impressions from those less experienced who might be lacking such structure and processes. 

With the enormous differences between headphones, the measurements still reduce the pinch of salt required for any subjective impressions: with the tiny differences between other pieces of equipment, surely measurements should serve at least an equally important role?

Any measurements always seek to reduce factors unknown to us though they may even open up other doors to investigate.  They can never eliminate them entirely obviously.  The state of headphone measurements is still not sufficient enough to look at the data and definitively predict it's sound 100% accurately even though we can get ideas about their sound.  Even the mere thought process of formulating how a graph will be perceived to sound is based on subjective experience btw.  Though the pinch of salt as you call it may seem a micro consideration, the affect of small differences in a dynamic system over a long period of time can be rather significant to some. 

This again comes down to a matter of personal values and metrics.  Does someone want a larger, possibly more expensive box to hear more of how Tori Amos parses her lips compared to something the size of a cigarette box?  Up to them.  Regardless, the differences are perceived to be there even if both would be classified as 'electronically transparent' by the standards of a certain acoustic engineer.  If there isn't something else contributing to greater perceived detail throughout the entire spectrum other than a prettier box and lighter wallet, that's some good shit I'd like to bottle and sell (I know many do).  My problem with that explanation is that it usually fails w/ most other gear that's even more expensive and pretty.  Hell, I don't find most of my gear good looking at all tbh.  In fact, it all pretty much clashes w/ each other in a very discordant aestehtic.  MF would not be pleased.

Like I said, no one here (to my knowledge  ) diminishes the value of objective data, just its comprehensiveness and definitiveness based on well seasoned and observed experience yet to be sufficiently explained. 

That's good.  Because many in the Obj camp have defined 'transparency=flat FR+low distortion'.  It's really not a straw man at all when there are those that fit the profile and regurgitate it.  It's a straw man for you, but not for others as they live and breathe it.

What else would you mean by transparency for an amp or DAC if not faithfulness to the input signal?  Flat FR and low distortion across the board (i.e. more than just THD @ 1kHz) are a pretty good marker for that.

See, you are equating those two metrics w/ representing 'faithfulness to the input signal' in it's entirety as a known absolute.  I and others do not based on experience.  When something like the O2 that measures better than my tube gear yet hides information on the recording I know I have more that needs to be investigated.  Of course, my tube gear and the tube gear i recommend don't measure horribly either and neither does the Leckerton UHA6S which also measures not as superb as the O2 yet also resolves more information. 

So pretty good marker?  Yes.  Absolute final, definitive marker?  No.  I equate gear A which lets me hear more information on the recording as 'more faithful to the input signal' overall than gear B that does less so regardless of specific metrics it was chosen to satisfy.

If people want to say gear A lets you hear more information on a recording because it has some flawed performance, well, show me and good luck proving that.    Till then, I'll keep looking for the 'X' factors while others remain satisfied in having it all figured out by resting on a specific null hypothesis.