James, here's some straight ahead advice for you, as you stated, "I'm searching for a solution that would allow satisfaction with all pieces I choose to pair at any given time. It's just one of those things and I do thank you for your input, but I couln't part with theses pieces, it's truly nice equipment."
Then expect continued disappointment. When a match doesn't work, it doesn't work, and any additional use of that match will result in diminished returns. Barring some problem with the equipment, there are poor matches in gear which will never yield optimum results.
Can things be improved? Sure; you can continue to try different cables including power cords, jack up the quality of the source with an upgrade DAC and a fine grade digital cable, and perhaps a speaker upgrade or roll tubes in the BAT. In the end you could spend a lot more time and money - and still get mediocre/unsatisfactory results, all for the sake of being stubborn. :)
A component match "mistake" is a mistake, whether we emotionally want to accept it or not. Maybe you bought these and do not want to take a loss on selling one, or they were in the family prior, or perhaps WFA (Wife Financial Acceptance) factors into things. Whatever reason, if your goal is the best sound then continuing to use that set is a hindrance to your satisfaction.
This certainly demonstrates that simply tossing together well known names does not ensure the sound will be to one's liking. It would truly be a shame if this occurred as a consequence of a recommendation and you spent a boatload of money. Tough lesson, but not fatal. There are many people here who learned the hard way, took their lumps and became smarter component shoppers over time.
BTW, don't think that you'll be sure to hit the jackpot sonically next time if you employ a "hit or miss" methodology. Random selection of gear is not nearly as likely to result in success as doing one's homework, i.e. making trips to hear gear, going to an audio show, discussing the sound of various equipment with owners and dealers, talking to the manufacturer if possible about recommended matches, and reading reviews (I am a reviewer).
Now, if you don't want to believe the bulk of this input, but want to be hard-headed about it, that's also just one of those things. The gear won't magically transform on its own; only a component change will cause that, as had been astutely presented previously. Putting together audio systems is a pretty good way of humbling a person, as those who think they're really sharp will find out quickly that just because we think we can assemble a killer sounding rig by our logic, reality often doesn't work that way.
If I've been too hard on you, my apologies. However, it appears like you're resisting admitting the combo was not to your liking and refusing to accept the implications (i.e. having to take a loss in selling a component, or having to return to square one in searching for another).
Once again, you said, "I'm searching for a solution that would allow satisfaction with all pieces I choose to pair at any given time." If you could find an elegant answer to that, you'd be a very wealthy man. I've got decades of experience in audiophilia and have built dozens and dozens of systems and can assure you that "solution" does not exist - unless you opt for putting up with what you deem inferior sound.
