I'm thinking similarly, but not via PCIe, but via USB: There are plenty of USB->VGA and USB->HDMI adapters that contain a dumb graphics card. So, embedd one of these and grab the video signal internally.

Thereby, plugging in just a single USB cable would deliver the power needed, keyboard, video and mouse. And bonus for an emulated USB-Stick/DVD drive.

What I don't know if these USB video cards are initialized during early boot and usable during the UEFI/BIOS phase. Is that why they grab the HDMI?