Question is -How do I "tame" an overly accurate response.So you are looking for an inaccurate response? Not sure I understand this.
Before looking for cables to effect the desired change, have you ensured proper speaker placement? Is the room treated?
I'm not sayin don't upgrade your cables. But in my experience, cables make very subtle sonic differences if at all. If things aren't right to begin with then cable changes make even less difference. My experience, YMMV.