The 645Z's shooting action during Live View is pretty similar to the way it's done by Canon. The mirror is already locked up so the sensor image can be delivered to the back LCD, so there's no need for separate manual MLU during Live View. Simply set up the shot, wait a few seconds until the camera is stabilized, then make the exposure. It works for AEB sequences as well.
If you don't want to drain the battery quite so fast, you can set up a shot in Live View, then exit LV and expose however you normally did before with MLU, self-timer, or whatever.