Realism in instruments how to achieve it?

What you're looking for is exactly why I keep my old ProAc Response 2's and use a 30 wpc tube amplifier, specifically a classic Williamson-type circuit that I built myself.   I mostly listen to classical and vintage jazz, and I like a rich, coherent sound, where instruments and voices are properly staged and grounded in a real space, not floating in the air or appearing from nowhere.  Realistic midrange reproduction is particularly critical for this effect.  So is a preamp, which, in my experience, can add weight and body to the music that you don't get from the music source alone.  For "bookshelf" size speakers, don't cheap out on stands--the ProAcs need a hefty stand to sound their best.  Cables make a difference too, but the speakers and amplification are, IMO, the two key ingredients.  

I like Spendors and Harbeths.  You might consider Fritz speakers, which I heard years ago at a show and offer the kind of sound I'm talking about.  I would try a medium-power push-pull tube amplifier.  Stick to 25-40 wpc.  More than that and you start to lose some of the magic.

A lot of folks here will scoff, but I'd be willing to bet that a properly-restored Fisher 500C would bring you more pleasure and realism than that Class D amplifier.  Whatever other limitations they may have, the classic Fisher, Scott and Marantz equipment was designed by people who went to jazz clubs and symphony concerts, and knew what real music sounded like.  I'm not suggesting you rush out and buy any old vintage piece from eBay, they have to be professionally refurbished.  But you might be surprised at how much musical enjoyment those older pieces can produce.  My goal in building my own amps and preamps has been to reproduce that sort of sound with updated components and refinements.

Suggest speakers with a relatively neutral sound.  Not warm or bright which can color the sound of instruments.  There are a lot of great choices.  I’ve had a positive experience with Revel speakers which are relatively neutral across the sound range. 

Congrats on upgrading to the BAT. As a long term BAT preamp owner and fan, and having recently upgraded within their line, I readily agree about the realism (inc "analogue" sound) their preamps deliver, having compared them with quite a few others.
 

Different people may mean or value different things which contribute to "in the room" sound. For me, one element is dynamics, where transients literally shock you, another element is spatial location and particularly a 3 dimensional stereo image with great depth discrimination and placement. Sometimes this results in instruments or vocalists appearing to hang in front of you in your listening room; on other recordings great reproduction of the hall ambience  (real or studio-created) transports you out of your listening room to that hall. Across all sources, so far I have best achieved the combination of dynamics and 3 D imaging by using my successive BAT preamps with valve power amps. Contrary to both expectations and design ideology of BAT, I have done this with single ended 845 triode power amplification and sensitive loudspeakers (Coincident Technology floorstanders). I considered changing the power amplification to a balanced configuration amp (either solid state or tube) rather than upgrading my preamp and sought advice directly from Victor Khomenko (BAT’s designer) and he actually encouraged me to go with the preamp upgrade despite the Balance to single ended connection if I like the SET sound. That’s NOT to say I would rule out changing to balanced (SS or tube) in the future to facilitate a wider choice of loudspeakers if sufficient finance became available and a home demo was possible and demonstrated the benefit of the upgrade combination. The choice might also be influenced by the type of music you listen to most.
 

I also am convinced that on digital sources the DAC choice is very important. I see R2R seems very popular on Audiogon but I wouldn’t rush at that spec as I’ve also read of downsides. I think a home demo would be very important. In general I’m a sceptic re cables and add-on tweaks as I think there’s a lot of snake oil out there commanding high prices. However I have been convinced in my system of the benefits of a good network switch and of some cable upgrades with respect to the soundstage, dynamics and sonic detail, and that "in the room" feeling. 
 
Being transducers (conversion of electrical signals to audio, or vice versa in the case of phono cartridges and microphones) loudspeakers, speaker-power amp matching, and speaker-room interaction (inc speaker placement) are also important for that "in the room" sound.

So in summary I think there are multiple parts of the equipment chain which help deliver what I imagine you’re after, and it is very difficult for others to predict which will have the greatest effect as a single upgrade in your system. The best way to work that out is home demo, if that’s an option for you. Nevertheless I think you’ve made a great first step for upgrading the realism of your system across all sources by upgrading your pre-amp with one from the BAT stable. 

Wishing you the best on your upgrade journey, and lots of fun on the way. 

From my perspective, your gear is starting to outclass your speakers. I would make some efforts to hear some other speakers and establish a budget for replacement. Short term, you might try going up a notch on your DAC, R2R might be a good bet based on your goals. You did not mention what you are using as your digital source/streamer. This can make a big difference as well.

The way the producer mic's the instrument and records it is probably 80-90% of it.  If it's not recorded properly, the gear that reproduces it can't bring out something that not in the recording.