Lots of opinions on lots of models, but if I had to give a general guide, I'd say:
BEST sound comes from Stax earspeakers, but they are not closed-cup like your Sony's, they "leak" sound so others around you can hear it, they look very nerdy when worn, usually come with their own power supply/amp, and are ungodly expensive. Never owned a pair, but have demo'd them. Not what you are looking for, but 'awesomely' good sounding.
:thmbsp:
Next in ranking:
Beyerdynamic
Sennheiser
Grado
Any of the higher-end models from these manufacturers will sound quite good. Which model probably depends on your budget, and which you find most comfortable to wear. Grados are not fully enclosed, though, which from your post might be a consideration.
If you can find a pair, you might consider vintage Pioneer SE-505's. I listen through them almost every evening to either a 2285B or a 2275 (very similar sound to the 2770 you mention). From the same sound period as the amp, and with the dual-drivers in an enclosed cup with volume and tone controls on each side, it sings pretty sweetly, and would be similar to your Sony but (IMO) nicer. Not quite up to the best of the brands mentioned above, but better than their lower- and mid-range products, and probably cheaper (if you can find a pair). You would need to do the DeOxit thing on the controls, though.
KOS makes some good ones, too. The only place I've used them (since back in the seventies!) was doing video voice-overs in a studio, not really hi-fi listening, so I can't comment on their limitations, but for canned music and spoken voice they seemed excellent reproducers.
