Been there, done that, many times. When comparing unbalanced vs balanced connections, I much prefer the total background blackness and lack of noise. Without the background grain, detail and resolution is greatly increased to my ears. To gain the "musicaliy" related to even order harmonics, I use tubed sources, and in spite of your claim that balanced connections eliminate this, I can easily hear the difference between a tube stage output on a player and an SS one.

After years of searching and testing gear, this is the sound that I like best. YMMV.