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 was in a similar situation last year, running the PS Audio Directstream DAC directly into my power amp.  It sounded good but not as good as I wished it did.  So I swallowed hard and bought their BHK signature preamp.  Sound is much improved, in just the ways you seem to be looking for.  I was able to get one for significantly less than list price from Upscale Audio -- pretty close to the price for a used one and to the top of your budget range.  You might give them a call and see what they are willing to do.  (On the other hand I am not in a position to say that this current model sounds drastically better than the used one you can get for a tenth the price. Haven't heard the 4.6.  Or the Schiit)
Why not mate a BAT preamp with your BAT VK-55? Seems like it would be a good fit.
I too follow a "no preamp" preamp approach.  The issues you are having are commonly talked about on the forums.  I have come across the Townshend Allegri+ variable audio transformer.  Its the best volume control I have found.  Its totally natural, adds no coloration and has incredible resolution (Using Apogee Scintilla Ribbons).  Could not believe it when I went from an external Naim dac to the dac in my Naim NDX streamer with the Allegri+.  Soundstage much better, timber around each instrument, soundstage extends past the speakers on some music, sound is very dynamic.  I could not be happier.  The Allegri+ is in your stated budget.  I am going to try a single channel version of the same--with one input and one output, and no internal connections--with constrained layer damping.  Single purpose device with no compromises and has remote volume.  These devices inherently address the impedance match issue which is the root of most of the problems with passive approach. 
nice tube preamp mated to SS amp is the way I would go ....
i would agree with this ..... I actually have croft 25r (tube rolled with NOS) which is a very sweet hybrid pre amp and way under budget going into ATC P1 / Harbeth 

it isn’t balanced however but my cable run is only 40cm.

of all the setups over the years this mix of valve early on and then tranny power has the control,  dynamism and smoothness I love. 2 years on I still tap along to music thinking WTF every few songs .... in a good way