I tend to agree with @raysmtb1 about wire size on this one, although the speakers and the amplifiers driving them will have a larger impact than the PC, IMO. You might try Triode Wire Labs Seven Plus, which is a 7awg power cord. However if you really want good bass, the addition of two or more well-positioned and integrated subs will do much more to get you there.
BTW, the TWL American Series cables are constructed using something similar to Western Electric stranded tinned copper wire, which many describe as having a rich midrange and full-sounding bass and so might help with your sensitivity to "brightness, harshness, shrillness", particularly in the higher frequencies. Also, equipment with a well-designed and constructed power supply is IME less susceptible to those undesirable attributes.