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?)