So quick update: after a few days of pretty heavy listening, it did seem to open up a little more (though some may be attributed to my ears adjusting to the sound). I did still hear a minor difference when the Iris was connected versus just running to the DAC, however.
I received the new cables from DH Labs and...it's a night and day difference. It's not even close. Removed what felt to be a veil over the sound immediately, along with improved the imaging, detail, etc.
While I've heard minor differences with different cables in the past with other components - like slightly blacker backgrounds with nicer power cables, etc - I've never experienced such a drastic improvement just from a couple cable swaps.
Some of it might be switching from a 1m cheap HDMI from amazon to a 0.5m HDMI, since the shorter length is ideal for i2s. Whatever it was, replacing the USB and HDMI cables did the trick and then some.