The G1X is behaving as advertised (it does not support HDMI output in rec mode).
The M3, however, should not have problems outputting HDMI signal in any mode. Things that I would look for include
- is the battery well charged
- is there an EVF attached
- does trying another cable help
- "Video system" setting in Canon menu
HDMI devices are allowed to consume some power from the camera's HDMi port, if that current is too high, the camera will switch HDMI off.
edit:
There's more. The camera may output interlaced signal, which some of those HDMI sticks do not support. Try connecting it to a TV/monitor.