What will a preamp do for me?


Missing in the chain below is a preamp - I use the DAC to control volume.  This is my only source and will be for some time.  What could I gain by adding a preamp?

I have Thiel CS 2.3s driven by a BAT VK-55, sourced by PS Audio PW DAC, with bridge II, mostly tidal.  The DAC serves as a preamp in terms of volume control.  Mostly Audioquest cables, amp power cord is Cardas Clear m, all fed by PS Audio upc-200.

I am am hoping to improve the highs, which sometimes sound smeared, too much sibilance; would like more air and clarity.  Loud rock sounds flatter, less dynamic than I’d like.  I am not willing to give up the deep detailed and beautifully resonant mids.  Willing to spend up to $3000, used is ok.  Totally balanced is a must.  Not currently willing to entertain the idea of different speakers - my goal is to make the 2.3s sound as good as reasonably possible before moving on to other speakers.  It’s easy to find a really good preamp in this price range, so much so I am almost paralyzed by the choices.  Aesthetix , Ayre, ARC, several BAT, Parasound and more all have apparently excellent models in my price range.  Patience would put Atma-sphere and PS Audio within reach.  Which is best for my situation?  There’s no way to audition all of these, how could I avoid getting on a preamp merry-go-round?  Or should I spend my money elsewhere?
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I have yet to get to the preamp auditions - I took elizabeth's advice and upgraded power cord for amp (Cardas Clear M), plugged it directly into the wall socket rather than the conditioner, and replaced the wall socket with a Furutech GTX-D(R) so far.  All modest but noticable improvements.  During the same time period, I added some isolation devices for the amp and source, and that is as far as I have gotten.  Isolating the amp with wood platform and Iso's cones and feet made the biggest difference by far.  In fact, now I am considering Gaias and Oreas too.  Next big upgrade will be upgrading the source to PSA's DSD DAC.  THEN I will move on to preamps, unless something else strikes my fancy in the meantime.
And almost forgot, I have been trying  some NOS 6SN7s, old Russian tubes from Upscale, in place of the Sylvania Chrome Domes that came with the amp, which has been interesting so far, probably worthy of another thread.  Bottom line - no big difference yet, but maybe still burning these old Russians in.  
elizabeth - the Goldpoint is a very interesting idea, one worth trying, had one in the cart before remembering that these cost about the same as the Schiit Freya.  Unless there's some obvious technical advantage in the volume control (neither use potentiometers, both use resistors) wouldn't it still make more sense to try the Freya?  I guess the selling point for the Goldpoint is no distortion, vs ability to influence SQ with the Freya?  
I know you said your budget was $3k, but for $4k you should seriously look at https://www.anthemav.com/products-current/model=str-pre-amplifier/page=overview
Good chance the DAC in this will handily outperform your PS - which you could certainly compare.  The biggest benefit of the room correction.  When you realize and resolve what the room is actually doing/contributing to your system, then 
Sorry, hit post before I was done...

then all the music you listen to will literally be like listening to it for the first time.