If you need 4x channels, it sounds like a job for QSFP? HDMI is already differential signalling, so you don't need to do that, but you might still need level sh

If you need 4x channels, it sounds like a job for QSFP? HDMI is already differential signalling, so you don't need to do that, but you might still need level shifting. Probably a box on the source end to manage DDC and strip HDCP.