Nevermind, found it, thanks for the heads-up.
Video > Video Dropdown (Upper Right) > Image Enhancement > Advanced
I had to disable both Film Mode Enhancement and Contrast Enhancement in Advanced and Skin Tone Enhancement in Basic, but the flickering and stuttering is now gone. The signal still fluctuates between 29/59 Hz but at least the Intel driver is no longer fighting it and trying to (poorly) insert its own image correction treatments.
These features should really be disabled by default and made to be more obvious. The UI is counter-intuitive and filled with far too much dead space. Features like this should be made to be more conspicuous, especially when they can have such a negative impact on end-user experience.