So the EDID / ELD must come from the AVR. It’s probably correct, but may be interesting to know what it says about the AVR’s capabilities, and how that compares to the documentation.
A phantom display means you could lose the mouse cursor off the main display? Or do you use display mirroring? If you disable the phantom display, then it also disables the ability to output audio, right?
Although DVI is supposed to max out at 165 MHz (single link), your graphics card may allow HDMI 2.0 to be output from those ports. My Titan X (Maxwell generation, same as the 970) has a DVI-I port that supports 4K@60Hz HDMI with audio (just like the Titan X’s HDMI 2.0 port), Dual Link DVI (165 MHz * 2 = 330 MHz), and VGA. So that might be another option to try for the TV or the AVR. And it might be better, if it does allow HDMI 2.0a like the HDMI port. The DVI-D to HDMI cable is passive, works with either as source, and should work with the DVI-I or DVI-D port. I don’t know if all such cables are rated for those speeds though. If not, then the display or audio may cut out momentarily. In that case, it might be best for the DVI to output the audio, since the phantom display could be set at a low resolution if you’re not using mirroring.
Right, S/PDIF/Optical is an old technology with much less bandwidth/features than the newer HDMI.