Yes, I would like just two things: AFL at the start for the entire set of shots, and autoexposure for every shot.
The camera only updates exposure when half press is pressed.
Normally, there is a delay between when you press half and when the camera is ready. Waiting for this will slow down shooting a lot, as waterwingz says.
However, the cameras make a "best effort" if you just push the button all the way quickly. This is usually doesn't focus well, but maybe in your case it would be OK since you only need exposure. I suspect this is happening with the camera that works for you now, but through a combination of bugs rather than by design.