I have the 3800 and can hear the difference between DACs, but certainly not to the point of a modern DAC sounding unnatural. For music, differences tend to be in warmth and AKM DACs sound warmer to me than ESS. Depending on the music, say techno vs a cappella singing, different DACs have their strengths. I have long used an external DAC driven by a streamer (initially Bluesound, but now a WIIM Mini since its introduction) connected to the 3800 via analog. IMHO, external DACs simply outperform internal DACs for two channel music and provide a consistency when moving from AVR to AVR. For music I own, I have long ripped my CDs and SACDs into FLAC and DSD files (including 5.1) and drive the streamer using Audirvana or the WiiM. Similarly for Tidal. The 3800's amplifier is better than my previous Yamaha AVR, so it has been an improvement for 2 channel music. I listened to Tidal through the 3800's internal DAC and SACD (via HDMI from the SACD player). It sounded OK, certainly not unnatural, but I prefer my external DACs via analog. My suggestion, is to plug in a good external DAC via analog and see if you are still getting unnatural sound. That will isolate the issue to your dislike of the Ti DAC.
To me, its important how you play two channel music and for me, it depends very much on the type of music. I generally play quiet music like vocals in Pure Direct mode, which turns off most electronics in the Denon and also turns off Audyssey or Dirac. Denon and Marantz have this great Mains+LFE mode, which allows you to run Pure Direct with L+R also sent to the subwoofer output. My SVS 3000 Micro sub has a fairly sophisticated DSP, with a 3 band parametric equalizer, and low pass filter, that can accurately tame low frequency room modes and therefore compensates for the lack of Audyssey. Currently sounds as good as I've every heard it. The worse sounding mode for this amp is stereo mode with Audyssey processing. Are you using this?
For noisy music, like Jazz or Techno, even big classical pieces, my current preference is Auro3D processing. To me, its a huge step from any previous two channel music processing. It adds 3D spaciousness, while retaining the forward vocals and clarity with Audyssey or Dirac processing, while utilizing all my 11 Atmos speakers and two subs. Definitely try it. I'm in the process of adding Dirac and DLBC. From what I've heard it will integrate the two subs better.