JRiver running on Dell PC USB output to Zodiac Dac to Integra 80.3 using stereo mode (to allow for room correction).
I currently watch movies through a BD player via HDMI to the Integra 80.3.
If I rip or watch music DVDs that have 2 channel output the results (through the USV DAC) are fantastic compared to using the onboard DACs of the Integra.
Your statement's contradict unless I'm missing something. From your setup description it sounds like you are using the balanced outputs or RCA outputs on the Zodiac and connecting them to your Integra so you can use Audyssey. If so, then the Integra is doing an ADC (analog to digital conversion), applying DSP including Audyssey, and then using the Integra's DAC's for output. Even the Direct mode of the Integra applies DSP (distance setting) so it is still using the Integra's DAC's. So no matter what you do (HDMI or Zodiac), you are still using the Integra's DAC's. I just read through the Integra manual and, unless I missed something, there is no way to do analog pass through without using its DAC's.
The only way I see for you to use the Zodiac as the final DAC is to connect it directly to your amps. Any differences you are experiencing in sound quality could be due to the high jitter associated with HDMI. You could try to go directly to the Integra from the Dell using a digital audio cable if the Dell is capable of digital output.
I assume you also have HDMI output from your Dell. If you want to keep your current setup and use HDMI vs the analog input, you should click on Playing Now and rename the current zone to "2 Channel" (I think the default is "Player"). Then right click Playing Now and click Add Zone. Rename this zone to "5.1 Channels." You can then go to Options > Audio > Output Mode and Settings and set it to use your HDMI output. You probably should use WASAPI or WASAPI Event Style. In the DSP Studio you need to set Output Format to 5.1 and Bitdepth to 24-bit.
Once you have the two zones setup, you can then just select the zone you want before starting playback. On the Integra you need to switch between whatever input you are using for the Zodiac and the HDMI input.