Nice troubleshooting. Frankly, the culprit(s) may be so many different component(s) along the signal path. I hope it is the pot and hopefully you can replace it if it comes to that.

I believe both the Schiit and the Transformer sound good but what are you missing with one vs the other or maybe both? To really know, you'd have to really listen to both and maybe a "reference" DAC - at no signal (to gauge noise), low volume and at high volume, with different inputs, music, file types, and bit rates. You'd also have to listen to each channel individually by unplugging one of your speakers and seeing how much audible cross-talk there may be. And you have to know what to listen for on a high resolution, high accuracy, low noise system.

House of the Rising Sone
Out in the mid or far field
Dedicated mid-woofers are over-rated