Yea, I dont have the DVX in front of me right now, but I know in one of the camera setups, there is a choice to put the camera on "standby" instead of power down. Sorry I can't point it out exactly....As for the timecode syncing....I don't know. Maybe you could use one of those timecode slates?
Edit: I looked at the user manual on Panasonics website, and I think what you're looking for will be found in the "other functions" menu, under "tape protect". In there, there should be a choice to put it on standby instead of power down. Hope that helps!