to the OP : finding cans that excel both in classical and in mixing will be next to impossible IMO.
I know several ppl who only care for the cd3k for classical! the cd3k is many ppl's favorite phone, for a very good reason!
it's a baby-R10 as I understand it, and I've owned the cd1k for 10 years(the cd3k is basically a cd1k w/ bells and whistles, same construction and drivers)....the trebles are sibilating to death, but also very hi-fi
there's no such thing as a perfect phone for every situation I'm afraid. I don't care much for classical music, and I very much enjoy my 770/600 for every kind of music I like(roots reggae/deep funk/ambient/indian music/movies/etc) but if my main focus were classical I would definitely grab a cd1k/cd3k again
but these won't output anything <60Hz, so mixing on them is completely pointless...and the cd1k/cd3k ear pads are pleather, that turn into zillion little black pieces after 6 months or so...that's VERY annoying, at least genuine leather is VERY durable and uber-comfy.
I like how everything in life always ends up being compromises
and I wouldn't expect a third party cable to turn your HD650 into a brand new phone, but that's just me