Low noise, neutral, high current power cord for wall to power distributor

It is impossible for us to make a recommendation. There are so many at this level, it will also be system dependent. I myself am thinking about it too, but under $1k. I am sure you have a few cords that you use with your equipment, you could experiment by placing all of them on your power distributor one by one.
There is also an opinion that the cord on the power distributor might be least important, it probably depends. 
For now I use Custom Power Cord Company Top Gun from the wall to PS Audio Premier regenerator. It was designed for fron end components but in some sense the regenerator is a fromt end component too. I also heard that some people had great success with Purist Audio Dominus. As for the total neutrality - it's an abstraction.

Inna- the PS Audio Premier is an AMPLIFIER, not a front end component, so getting an better, high current capable power cord is going to give you a high level of improvement in performance.  I would strongly consider the PS Audio PW-12 power cord for this as well as for Pani's application.  Good Luck!

Yeah, I know. I tried to put the Dominus on the PS Audio and the Top Gun on the amp and it was worse. I was thinking about PS Audio PW-12. Still, Top Gun works pretty good in my system, dynamics is good, better than with PS Audio Plus cord that I had on the regenerator before.