It's good that you stated your preference in terms of music and open vs. closed. However, I think it would help even more if you gave some more details regarding what you particularly value about your AT's (I haven't heard them), for example, or what you think would be important for you: neutral sound, fun sound, lots of detail, warm and relaxing sound, soundstage width / depth / imaging is / is not so important and so on.
Does your budget apply to the headphones only or to the headphones + the amp? I like my Stax phones quite a lot but only with my rather cheap source (I have tried only a few, none more expensive than $1000), so I'd be tempted by the 2170 combo in the first case (or perhaps a NOS 2050 - recently discontinued and cheaper) or by the 407 phones from Japan + either a diy amp, a second hand one or a 323 amp with correct power voltage (could be quite expensive, it's $1200 from the local dealer in my country for example). The 2050 / 2170 are nice systems because they are somewhat portable and can be bought from Japan without the voltage conversion problem of the "full size" Stax headphone amps - you can buy a cheap power supply for the required 12VDC, use a lead-acid battery or build yourself (or have built for you) a somewhat fancier power supply for the remaining ~$200 from the total $1000 for the whole system. Many have commented the old 2050 system was great value for money, and so should probably be the new 2170 too.
Listening before buying would be of course a good idea, and so would be buying used. Anyway, at least take some time after you buy to really get to know your new headphones, try some different sources and interconnects with them if you can (especially if you buy Stax), get used to them a bit and only then decide whether you are satisfied with them or not.
Good luck!
