Was reviewing some practice video, and finally found out what I was doing wrong.
When I would step into the shot, my left foot was going towards the shot line. This was causing my cue (and I'm assuming vision center as well) to go across the line. Hence, always putting right spin on the ball, when I'd think I was hitting center.
Solution that seemed to work for about an hour's worth of practice today...
Stand more square to the shot. Back foot at about 45 degrees. Now when I step into the shot, my left foot is going more up and out (to the side). This allows my head to drop straight down.