Turning toward the power supply it's easy to see that stock unit is supplied with 12V and 3.3V which is not fully compatible with the requirements of the compute module - namely 5V, 3.3V and 1.8V.

Strictly speaking you can run the compute module with only 3.3V and 1.8V but 5V is needed for HDMI and USB.

Since I've successfully used a circuit based around a PAM2306 regulator in the past I'll plan on using this to supply everything from a 5V source.  As I don't like playing with mains voltages I might hide a standard (read safe) 5V charger inside the power brick.