Mellow speakers

Sorry for typo ... ". I am afraid some of the dynamic speakers like vandy and quad may sound mellow to many people"

I meant vandy and audio note.

I have the same sensitivity as you. I cannot stand that edginess because it hurts my head and ruins the musical illusion for me. I have spent years fixing it and i finally have a system that sounds amazing and more like real music than ever before. As you may have discovered each component can contribute to the problem or the solution. I have found there are detailed/harsh speakers (most audiophile speakers sound this way to me partly because i am sensitve to it, and partly because too much treble detail is what many audiophiles want, because they equate that with a more live and realistic sound. Then there are more balanced speakers, like vandersteen or old Proacs or Snell Type A1 (one of the most amazing speskers ever). But even they dont fully remove the edge, especially if you listen to recordings that are not perfect. This is all, of course, just my opinion! 
So, in answer to your question I will give you one unfailingly mellow speaker, the Spendor S100. It is incapable of sounding harsh and has a magic midrange. I found over time is was almost too dark, even for me... But it fits your bill. The other speaker is my current reference and will be for years: Quad esl-63. The quads are so musical, have the best midrange i have ever heard, and for some reason the way they reproduce treble is different that any speaker i have heard. They just seem to avoid that edge but still present treble energy is a convincing, real way. I bought a newly refurbished pair from Electroststic Solutions in Kansas City three years ago and they are amazing. I recently bought a pair of Audio Note AN-J spe speakers to possibly replace the quads amd after head to head listening the darned quads won again. I kind of wanted the Audio Notes to win because they mate better with my Shindo amp and look better too. But as wonderful as are the Audio Notes in terms of dynamics, tonal balance and musicality, they still have too much treble energy for me and sounded like hifi moreso than the magical Quads. I am afraid some of the dynamic speakers like vandy and quad may sound mellow to many people, but may not do enough to solve your need, if you are like me.

Anyway, feel free to send me a private message if you would like to talk more. I have thoughts on other components like DACs (I was thrilled to find out none-oversampling dacs like Audio Notes take away much of the digital edge, for example).
Stu

JohnK makes a great point. I too have found that the relative tonal balance from top to bottom can give the impression of brightness and cause fatigue, when what is really wrong is lower mids suckout and/or lack of lower frequencies to balance the presentation.

Psag: i respect your opinion and each person should listen to whst gives them the most enjoyment, but I am in the opposite camp after 35 years as an audiophile (started when i was 16!). Neutrality to the recording doesnt matter at all to me because most recordings are flawed and do not represent the original musical event. I want components that provide the best illusion that the recordings of music I love seem real to my brain. It is a very personal experience and subjective. Enjoyment, for me, trumps (these days i should find a different verb) any notion of accuracy or neutrality. So i pick music i love, amd build a system that plays it best, rather than the reverse.