Replying to my own question: Seems like it doesn't look very good for HDMI-out on the Pro1X, at least when it comes to alternative OS's.
Unsurprisingly, I can confirm that my all-in-one UGREEN USB-C dock, which works flawlessly with the Pro1, does nothing regarding HDMI when connected to the Pro1X (also Ethernet does not work with the X btw ...).
After a bit of reading, I wonder whether the solution that was presented during development of the Pro1X is actually using any native "HDMI-out" features of the SoC. Rather, it seems to implement an MHL interface and needs a proprietary APK