Okay, quick update. I did found out that the stock shielded power cable that I had had the shield's drain wire connected to both ends of the ground. Apparently, this is required for UL purposes. I've been told that this isn't good for audio purposes. So my listening tests did match up with what's going on.
Now that I have first hand experience that power cables can sound different, I question how various audiophile shielding power cable are connecting their shields. Are they connecting one end (which end), both end, no end? Is it possible that they are liking something that might actually be a bad design? I tried looking around various manufacturer's page and nowhere did they specify how the shield was connected.
From a limited survey, it seems that the Audiogon crowd seems to like their various shielded cords. On the other hand, the Naim and Linn crowd generally prefer their unshielded cables and for similar reasons as me. The shielded cables can sound good or different initially, but over time some you become aware that something is off here. When going back to the standard unshielded, it initially feels dull or boring but it has correct balance and doesn't bother you in the long run.