When your running, tap L1 to turn on/off auto run. When your auto running, you can move the camera around and you'll still be moving in a straight line.
Im also on a ps4 and use the legacy camera. Unfortunately, because the camera is always following you, you're gonna have to keep the left joystick tilted ever so slightly for it to stay at that 90 degrees. you get use to it.
I also think that somewhere in the system settings you can change the speed that the camera moves.