What I was looking for I'm afraid I could only describe in an ambiguous manner because I'm a novice. I would sum it up this way: Mids and highs of Grado SR80, a tad less sharp but clearer. Plus bass a la ATH-M50, but not so much that it would eat up the mids. More bass extension and wider sound stage, if possible.
I've tried and returned half-a-dozen cans. Senn Amperior and Momentum over-ear didn't impress me. Yamaha something-huge was returned the next day. Tried B&W P7, they're not for me and too expensive too. ATH-A900X was suggested to me in some other forums, but I was iffy on its double-wing headband type.
After reading many rave reviews here and elsewhere, I bought NAD Viso HP50 yesterday. I was impressed. After just three to four hours of listening with iPhone5, I am sold! Can't wait to try these babies through my Maverick D1+ over the weekend.
My search is over.
(Oh, wait, a minor gripe: What's up with the squarey-curve corner of the headband?)
I think by squaring off the headband they allow for more even pressure across the entire can on your head rather than more pressure at the bottom than the top. At least that is what I've heard.