Do you own Salks now? If so what type? The reason I ask is to get some kind of idea what your really looking for.
No headphone I have ever owned or listened too replicates the soud coming from any 2ch stereo setup IMO.
Now some headphones and setups do a really great job of reproducing music very well in a very special and oeasing way, but its very different.
Now the being different does not mean the presentation is not good or great. Some headphones and associated dacs/amps can reproduce sounds very accurately, very pleasing, with good tonality, good soundstage, imaging etc...but different than speakers in a "good" room well placed etc.
I do spend lots of time with headphones and dacs and amps. Much is DIY.
But back to headphones and the cost....you do not need to spend megabucks here, just like owning a pair of Songtowers vs Exotica 3's...the exprience will be different but IMO both could produce a wonderful satisfying experience.
That said several companies make headphones under $1000 that are absolutely great as far as headphones go. There are many attributes that come to play when I picked out headphones.
Like comfort, impedance, what other ancillary equipment would you need to have a chance of working well with them, tonality, soundstage, sensitivity etc...
Then after buying over a dozen sets of headphones, it comes down to YOUR personal preference and listening to each and they all sound different and similar in many ways.
My number one recommendation after ALL this time, money and experiences to get to a really good setup with headphones would be: Wait...wait....wait...
But remember that there are other combinations that may provide you a similar experience, but after many,many cans, amps an dacs there is one setup that IMO really stands out as a great example of how well this technology is to date.
Sennheiser HD600's, $286 +/-. So you have a good chunk of change left over in your $1000 budget.
If you want to spend ALL your money on the headphones, then a set of Beyer T1's, Audeze LCD 2's, or Sennheiser 660s....gosh there are so many more, but each is different in those above mentioned attributes.
I could be very happy with the HD600's, a Bottlehead Crack (with Speedball) amp with a Schitt Bifrost MB DAC...you cound stop right here and be very pleased.
Now does this sound as good as or better that a pair of Salks or any speakers...you will have to be the judge of that.
Note: This topic has been discussed many, many times and there is a HEADPHONE section on this website that might be more appropriate for this type of discussion.