What is the best sounding DAC at $2000-$4000?

The Ayre QB-9 is an excellent choice and fits within your budget.

Have you considered the Ayre QB-9? It fits your spec, and is very highly recommended and reviewed. I really enjoy mine. Heck, I'm enjoying it right now!

There is no definite answer since it depends so much on personal preferences and system synergies.

But to my ears and in my system the best DAC I have heard in that price range is my Level 2 PDX:
http://www.lenehanaudio.com.au/index.php/products/pdx-usb-dac.html

The only thing I have heard that bests it, and I have heard and owned quite a lot, is my much more expensive Playback Designs - and then only by DSD - the PDX still bests it with PCM.

Although I haven't heard it personally people whose ears I trust tell me the AMR is up there as well.

But really what you should be doing is trying to do is hear as much as possible in your system and making up your own mind. I know the Tranquility DAC guy offers a free in home trial and you should avail yourself of that - I own one and its very good. Other quality manufacturers like Empirical Audio have similar offers.

If you were out in Australia I would lend you my PDX but I am afraid sending stuff overseas is a bit too expensive and the risk of damage quite substantial. I lent a speaker I own and wanted to sell to a guy in the US and when it came time to return it (he didn't want to buy it) decided to send it to a magazine to get reviewed first just to see what they thought. On the way over one of the speaker terminals got bent. That meant I couldn't on-sell in the US and will have to pay a large sum of money to get it sent back to the manufacturer to be fixed. You live and learn.

I have also been privileged enough to be at comparisons of a battery powered Hiface directly feeding the DAC chip on the PDX. A number of top quality transports such as Wadia were tried against it - it MURDERED them all. Right now, when done correctly, USB is the way to go - but it must be done correctly - unfortunately most aren't - however the PDX, Tranquility and Empirical Audio's Overdrive DAC is.

Thanks
Bill

This one only has a USB input so not sure it would work for you, but it's also "only" 900 bucks and seems to possess many of the qualities you're looking for if you put any credence at all in reviews (I know, I know). I think the reviewer bought the review sample, which at least says something, and I believe it was also positively reviewed in Stereophile. I thought the Ayre recommendation was a pretty good one too if you're looking for a smoother, more analogue kind of sound. Anyway, best of luck.

http://www.goodsound.com/index.php?option=com_content&view=article&id=249:wavelength-audio-proton-digital-to-analog-converter&catid=56&Itemid=37

Getting the PWD MKII would offer the additional benefit of network streaming if you get the bridge - this will sound better than USB. I would get one used and give it a whirl.