One option not mentioned yet is to get a basic equalizer like a Schiit Loki Mini (4 band) or Lokius (6 band). They are inexpensive ($150/$300 respectively) and can be switched in or out of the circuit without twisting the knobs. You could then experiment as much as you want to better tune your Luxman to your liking. The loudness button on your amp only gives you a single fixed version of what they think should happen and it sounds like that doesn't match very well with your expectations. And, there is always the digital option with Room or other devices, but that's a bigger change to your source than just inserting a Schiit equalizer.
Just another option for you before you throw some big dollars around.