If at all possible, I would recommend that you try to sample any headphones you're considering for purchase.
Head-Fi can be very confusing since so many of the opinions and recommendations are obviously very subjective.
There are so many variables that need to be taken into consideration, taking anyone one person's recommendation could
easily end up being a costly mistake. Also, you might be better off to upgrade your amplification first, which would enable
you to get a more accurate idea of any headphone's potential.
Once you reach a certain level, sound signature can be just as important as"SQ" which is by nature subjective.
Unfortunately, most classical is actually recorded relatively poorly compared to many other genres due to the poor acoustics
of many classical concert venues. Also, it is more challenging to record an entire orchestra in comparison to a performance
with fewer instruments/voices in the controlled environment of a modern recording studio.
IMO, the "warmer" and more "forgiving" HD 650's match very well with most classical recordings.
FYI, in addition to the 650's and 702's, I own several other flagship models from Sennheiser, Ultrasone and Grado.
They all have different signatures, but to state which ones have superior "SQ" would be nothing more than a subjective
opinion. If you want to keep your budget under $1,000, I believe the 650's (or anything else you like in your price range)
and a decent amp would serve your needs very well.
Spending more than that would probably put you in the realm of diminishing returns.