@haimr , what is at the output of your Lumin DAC? -- A transformer. Why? To give it a transformer sound, most associated with tube amps. There really is no other reason to use a transformer. You can’t avoid what that transformer is going to do to the signal. Everything else may be state of the art in the unit, but put those transformers in, and it no longer is. I am sure there are lots of pseudo-technical reasons around "best way to achieve balanced output", etc. but they are hardly the only way. Here is the data sheet for the exact transformer:
http://www.lundahl.se/wp-content/uploads/datasheets/7401.pdf
Unfortunately only a single point distortion measurement. (Note the op-amps in the circuit are usually good for about 0.005% so they are not the main contributors in the test circuit). No matter how good the ESS DACs are, this is the bottle neck.
The transformer is going to give them a house sound, and you may absolutely love it. I hope you do. But I am with @azwill here, when you are in the realm of DACs with a house sound, you are in realm of personal preference and that preference may change on a music by music basis, and possibly other pieces in your system and with the CAT amp it may be too much of the same thing.
You don’t need a new/different DAC, but you may find you prefer a different DAC matched with the CAT for some music.
I think you may own the highest WAF rated floor standers on the market.