With the combination of, Luxman 595, Eversolo A10, Focal... I would expect you would be looking for a warmer more musical sound. Those taken together push towards the detailed and trebly side of things. The Luxman solid state sound is very shiny (every time I hear one, that is what comes to mind).
If it were my system I would look to replace the preamp first. Get the core to be warm and natural. Moon is not warm... it is resolving and somewhat dry.
With your Focal speakers (also resolving and a bit hot on top) you want a warmer more musical amp / preamp. The new Pass integrates are really good. They are getting surprisingly good rhythm an pace from a solid state amp that is resolving but not overly romantic.
If it was me, I would look at an Audio Research or Conrad Johnson Preamp and a Pass XA amp or if you want cleaner faster Xamp. Although realistically tube amps will get you closer to the real thing.