Hey OP, what you describe does not make much sense. Sounds like you may need some mains clean up and there are many products that will help. You are under the mistaken impression that heavier/ thicker cables will swamp the system with massive amounts of current. It does not work that way. Also do not assume that if wire is able to deliver, say 10 amps (a steady state rating) that it will be adequate for transient dynamics which is what music is, as you know.
A component will only draw the current it needs dependent on the demands of the system, in other words if you connected to the mains with heavy duty truck battery jumpers the system would use the same amount of current.
Start eliminating and narrowing your search by simply connecting a multi-meter to your amplifier terminals with the meter set to DC. Should read no more than a few millivolts and ideally zero.
A word of caution! Any cable thread should carry a health warning. Cables make a difference and to me power cables carry the biggest rewards.