the power supply isn't the problem from what my experiments have shown. Even when using batteries, the same action still causes the camera brown-out.
Because you are not supplying enough current! The problem is you dont know what everything is rated, (what needs what) The LCD could run on 12V @ 5A, the camera could be running at 12V @ 3A, and the motor could require another 0.5A. (spitballing numbers)
Your power supply can ONLY produce 12V @ 7.5A, whereas your componets may need 8 - 8.5A. It worked correctly last time when you had 2 power supplies because you split the current. Your single power supply can not handle everything.
You need to find out EXACTLY what each part needs to opperate properly, then you get the power supply to run it all.
Not the other way around, unless you get all new low power components.