Ok, update: I paralleled the OSD and Unify with the Naze off the BEC, and I'm getting really grainy footage; the writing from the OSD is grainy too, and the colors from the camera are very weird. List of current connections:
The camera positive is wired to the battery positive
The camera Ground is wired to the OSD
The camera video is wired to the OSD
The UBEC positive Vin is wired to the battery positive
The UBEC negative Vin is wired to the battery negative
The UBEC positive Vout (5V) is wired to the 5V rail (extra motor pins) on Naze, the power to the Unify, and the OSD power
The UBEC negative Vout is wired to the ground rail on your Naze, the OSD negative, and the Unify negative
The Unify video is wired to the OSD
The camera positive is wired to the battery positive
The camera Ground is wired to the OSD
The camera video is wired to the OSD
The UBEC positive Vin is wired to the battery positive
The UBEC negative Vin is wired to the battery negative
The UBEC positive Vout (5V) is wired to the 5V rail (extra motor pins) on Naze, the power to the Unify, and the OSD power
The UBEC negative Vout is wired to the ground rail on your Naze, the OSD negative, and the Unify negative
The Unify video is wired to the OSD