Power conditioning for multiple dedicated circuits

My non-technical contribution at this point- I have done a number of rooms over the years with dedicated circuits and they cannot, at least where I lived by code, be entirely separate from the main household electrical service. (If you live in a place where you can have entirely separate service entrances all the better but there are still limitations). That said, none of the systems, save the present one was immune from noise elsewhere on the lines in the house. Perhaps this is due to shared ground, maybe the answer is different for different kinds of noise-- for example, at the designer/manufacturer’s suggestion, I swapped the lithium battery packs in my line stage and noticed a feather or two of dust under the batteries which I removed- I had an intermittent burst of static occasionally that was driving me crazy.
Other noise, apart from tube rush or simply what you think you are hearing as background to program material, whether digital or analog, may not be as evident until you eliminate it. But, there’s the rub-- I haven’t heard the latest crop of power conditioners, and depending on what you are hearing (I’m not there), I don’t know if your power can be improved. If you have the ability to experiment with the right to return at minimal penalty, you have some freedom to see, including what each component is arguably contributing to what you are hearing by swapping conditioners in and out on different pieces. I never used them on amps-- (well, I did try them, but not for long). 
I have no competence to comment on the wiring issue, you are in good hands with @jea48 .
Once you get that sorted, I think the next important thing is to look at your system, make sure everything is working as it should and consider optimizing room position. This is less about spending money and more about learning and experimentation. Jim Smith’s book is often cited as a good starting point.
I can certainly hear differences over my system, and even small changes are discernible. Such changes may or may not be improvements in the lucidity of your musical experience. So don’t equate different with better until you have listened for a period across a range of music.
That’s all I got.

Well, a little late now, but you would have been better off running 220V lines and putting a transformer in the room. You would have lower voltage drop from the length of the cables, and better noise isolation thanks to the transformer.

If you must go this route, I recommend Furman strips or conditioners with LiFT and SMP, or Tripp Lite Isobar Ultra as affordable ways to reduce noise.

Eric, I always had an interest in doing just what you recommend here. In fact, I believe that the Richard gray Company used to make what was called the 'Power Station'. You give it 220AC, it uses a step down transformer, and produces 120AC balanced power IIRC. Of course it was massive and too expensive for me, but it did catch my eye.
 Long ago, I was able to run 2 separate 120 lines out of phase with each other, using some equipment on one line and other equipment on the other. That is why this thread appealed to me with the ganged breaker doing the same thing. Can't say whether or not it is an actual benefit to it, but want to believe that there some out of the box possibilities to be groomed from it.

I have been thinking more about my 12/3 wire configured for two separate circuits.  There is a single neutral and ground wire going back to the panel.  

Does this matter when all neutral and ground wires in a house are going back to their same respective bus bar?  The neutral and ground bus bars are even connected within the panel.  

I would like to understand how two of each returning the panel compare to a single run.

Richard Gray's power stations were resonant filter tanks, widely available for 110 VAC but I'm sure they made at least 1 version that was 220 to 110.

I believe Equitech makes a number of suitable models today.