The Grado HP-2 is the only truly neutral headphone ever made, as far as I can tell. If you really want neutral, you'll have to suck it up and get ahold of one. And then you can combine that with a neutral tube amp if you want to add a touch of warmth, or a neutral SS amp if you want more precision.
I do think neutral exists. Because you can hear it when you listen to the HP2's- it is this feeling that the headphones are not adding anything into the music, no salt or pepper or spices, just straight up meat and potatoes!

I think many people mistake neutral for analytical or resolving. But neutral to me has nothing to do with detail, it is about tone, and about sound signature, frequency response. Trumpets must sound like trumpets, everything must be produced evenly throughout the spectrum....