Not only PS, If are resampling while playing back then it also affects sound. I tried all in my setup and found that oversampling above 24/96KHz makes high and mid too sharp and fatiguing. Lower makes it muddy, and at 24/96 it was perfect.On the whole, perhaps the switch mode PS introduces noise into the circuit, which gives a peculiar color to the vocals and highs. You solved that with the battery. In my unit the DAC is doing well, but the 3116 Amp has the issue.
BTW Let us know about your supercap experience. When last i tried, it did not hold that much energy.