Getting more from my DAC

I need some advice. I've put together a mid-fi office system over the last few months:

Sony XE500 CDP acting as a transport
MSB Link DAC III with 24/96 upsampling
McCormack Micro Integrated Drive amp with upgraded PS
Tannoy System 600 nearfield monitors

Toslink cable between transport and DAC. Ratshack gold series interconnect between DAC and amp. Audioquest Type 6+ wire between amp and speakers.

I was fairly happy with this system until I tried connecting the Sony CDP directly to aux posts on the amp and switching back and forth between the CDP/DAC combination and the stand-alone CDP. On a straight A/B comparison, using the selector switch on the front of the amp, I hear almost no difference, even with well recorded piano music/female vocal/jazz.

This is disappointing. The amp is low powered but pretty transparent, I believe - as are the speakers, which were designed as pro monitors and have a reputation for being revealing. So why aren't I hearing a more perceptible improvement - change, even - in the sound when the DAC is introduced into the system?

Are my crappy cables strangling the DAC? Is the transport too cheapo to let the DAC do its work? Do I need to follow the MSB/Modwright upgrade path before the DAC will really shine in my system? Or is the whole system a bit too bargain-basement to benefit from a decent DAC?

Words of wisdom gratefully received.