Some observations and contemplations.

Good amps in general have very low distortion and a flat FR over the entire audible range and beyond (but appears not to matter).
They don’t react to loads too much unless limits are reached or output resistances are relatively high (a big no-no).
The specifications and performance in general are (objectively speaking) factors better than the best transducers out there.

ALL headphones out there vary at least several dB’s and all show musch higher amounts of distortion, resonances and may behave differently on amp A compared to amp B.
I put to you that ALL headphones are flawed (even the mighty HD800 and AB1266) in mechanical, electrical and acoustical sense in a far bigger way than a decent amplifier.
How about perception itself ?
It seems to me that the transducers and listener are the weakest links based on these observations.

IMO it really doesn’t matter if one seeks an amp to match a specific headphone or a has a specific amplifier and is looking for a headphone to match. 
In the end it all comes down to a combo you end up with based on your philosophy.
I would even dare to say that both methods are limiting as in both cases one assumes the headphone OR amplifier is 'the best thing out there' and merely needs to be matched with the other 'best thing' to reach sonic optimality.

After all if one has a ‘best amp’ that only needs a best headphone that best amp could only be considered best if one had compared it to others with the same (or a limited number) of headphone(s).
The best combo would thus already be known as it must have past evaluation along the way.
The same is true for the opposite direction of looking at things.

Then there is also the question that when one has determined which is the best amp EVAR and best headphone EVAR (not tested in that combo) whether or not that combo will also produce the best sound EVAR ?
And to WHO will that be best sounding as preference is also important and perceived SQ is not an 'absolute truth' but an opinion that may or may not be shared with a select group of people (mostly in close proximity).
What is liked best by person A may NOT sound best to person B is what I am getting at.

This is definitely a different philosophy than finding the "right" amp for your cans, but I would think of it as equally important. There are several factors in the SQ chain but some are seen as more important than others. HF seems to believe that the headphone is the most important part of the chain, hands down, no questions asked. A setup consisting of the ODAC>Emotiva mini-X>HE-6 is put on a pedestal over something like, say, a Bifrost>Crack>HD600. Sometimes I'm convinced that, aside from the theory that the headphone means more than anything else in the chain, the price tag on the headphone is equally important to some hobbyists.

As far as your predicament, having a great amp without a great headphone to pair with, getting a great scalable headphone (aka Sennheisers) makes sense to me!

My 2c:

I find lesser transducers (loudspeakers and headphones) much more acceptable when the upstream (D/A and amplification) is top notch. Once you're at the point of a "solid" upstream (definition of "solid" might vary from person to person), you'll get tangible benefits by moving up in the transducer realm. Or at least, that's the path I'm on right now.

I've been thinking about this a bit lately as a type of user-centered technological experience.  Ignoring speakers: it seems strange that the most modular component (headphones) would be the object that often obtains the most rigid fixity in an audio chain. Larger desktop and home sources and amplification are often much more physically inert; they are also (pretty often) more expensive than the headphones they are driving. So odd that these pricy and inert components get swapped around so often.

This is definitely a different philosophy than finding the "right" amp for your cans, but I would think of it as equally important. There are several factors in the SQ chain but some are seen as more important than others. HF seems to believe that the headphone is the most important part of the chain, hands down, no questions asked. A setup consisting of the ODAC>Emotiva mini-X>HE-6 is put on a pedestal over something like, say, a Bifrost>Crack>HD600. Sometimes I'm convinced that, aside from the theory that the headphone means more than anything else in the chain, the price tag on the headphone is equally important to some hobbyists.

While this is a bit cynical - imagine that  - I think a lot of this certainly rings true. But high end amps and sources have much higher price tags, no? I don't think it's entirely Veblenesque conspicuous consumption or status performance play, though that's certainly part of it. I think that most end users simply bond with their headphones because headphones are worn. In an audio setup, headphones as their most frequent point of physical contact. People bond with their headphones not only through sound but through ergonomics, size & weight, fit, aesthetics, general tactility, etc.. Amps and Sources on the other hand have aesthetic and interface properties, as well as brand loyalty aspects - but are not necessarily worn. [Edit: see mkubota1's post who pretty much says the same thing, but minutes earlier in time.]

For me then, the companion question to Marv's is: why don't most hi-fi users bond the same way with their amplifiers and sources? Because I actually think that this might differ when we discuss stationary rigs (home and desktop) vs portables. When the source and amplifier become more modular and carried...

I'm going to turn this argument around to this: Getting a headphone which will make make the most of an amplifier / source.

So instead of this tired argument "you need the right amp with the HD800" which seems to rub some people the wrong way, what about "the EC 4-45 needs the right headphone" or "needing headphone Y for amp X"?

...these questions become much more common. When I look at that demographic, even on Head-Fi, I see that people *do* wonder what headphone to pair with their CLAS, Leckerton UHA-6S MKII, Apex Glacier, DX100, AK240, HiFi M8, Pico Slim, Pelicans etc etc etc.