With your budget, you should consider the Focal Utopia.
I have the Focal Elex from Massdrop and they will give you the kind of sound signature you're looking for. The Utopia will give you more of what the Elex does. I listened to some Utopias, and they are beguiling. I have Harbeth Super HL5 Plus and P3ESR, and of the dozen headphones I have, I would say that Focal headphones come closest to the Harbeth sound.
I wouldn't dismiss Sennheiser. I have the HD800 and like them very much. The HD800s is supposed to have tamed some of the "brightness" that some complain about with the HD800. I have not heard the HD800s. The $200 Massdrop Sennheiser 6XX are probably my favorite headphones, but more for reasons of comfort.
I have not gone up the Hifiman line, but I have the HE560. They have a similar, but more neutral sound signature than Audeze. My Audeze headphones are more detailed, and they do more than just bass well. The LCD-4 are pretty amazing and have a great midrange.
Lastly, the Sony MDR-Z1R deserve consideration. They sound very similar to the LCD-4, at about half the price and are a lot more comfortable. The LCD-4 is probably the heaviest set of headphones I own.
For amplification, I have a Simaudio 430HA. If you do get the Hifiman headphones, consider their EF-6 amp. It's discontinued, but you might be able to find one at a reasonable price. Sony's headphone amp is really good also.
Forget about "soundstaging". You have two speakers on the side of your head. You simply can't get the same kind of imaging or soundstage that you get with speakers. Some headphones will do a better job than others of not making this apparent, but headphones by their nature will give you a completely different listening experience than speakers. I rarely use my headphones anymore, in large part because my two channel systems have gotten so good.