I agree, with new cabling and a 12.71V resting voltage, I don't think the problem is your electrical system. Heat will cause the screen to go "black" though, but that's not what you describe and it normally corrects itself when things cool down.
You ARE plugging the Gryphon into the OBDII port with the ignition ON, right?
If so, I think I'm out of ideas and Bill will have to come to your rescue.
- Jack