The problem with using the center part of the limbs is that most cams don't have the string track right down the middle. The are almost always to the left of center.
Can you be "out of centershot" with a dropaway??
You should set up a drop away the same way you set up a conventional rest. I always set my rest up by eyeballing everything, then shooting through paper to see what tears I have. My main concern is verticle tears. Left and right a smidge isn't a problem as I do walk back tuning, as mentioned above, to dial in my centershot.
If you are shooting groups further and further left or right the farther your range is, its most likely center shot. If everything is going left more and more as your range increases, simply start moving your rest to the right, a little at a time. Its amazing how much 1/16th movement can make a group move.