I understand your desire. it is clear that you have made careful choices of compatible equipment that have delivered the excellent sound you are getting. Each of your components are tuned to be on the lean side. From your description of the way forward seems to play towards the sound qualities I strive for.
I had a very high end system that delivered great detail and dynamics, not unlike yours. One day I upgraded my headphone system with a high powered 300B tubed head amp. I was blown away. It sounded so great, so musical, natural and powerful I wanted more so I went to my main system and turned it on. My face turned red with disappointment… it was lean and flat, nothing like the beautiful rich sonic quality of my headphone system. It had little music or midrange in it. That began a complete system upgrade. You can see my systems under my user ID. Both systems are very musical and natural with great midrange bloom. I have to drag myself away each day… and I often listen for two or three hours.
Your Aurrender is great… a keeper. The dCs and Luxman are both very lean components the are low on mid-range bloom and rhythm and pace. If I were you I would start by swapping out the integrated amp with an Audio Research LS28se and VSI 80. If you are not open to tube amps… still get the Audio Research LS28SE and look at a Pass XA amp. Then swap either the speakers for Sonus Faber or the dCS for a warmer more natural DAC.
Lots of possible solutions are possible.