When I did this exercise a key learning was that my driver swing flaws were showing clearly in the strike patterns as pointed out by @Valtiel. I did some practice with video and was able to find the center of the face much more consistently.
I did it by moving away from the ball a bit and getting my back less rounded at address. I then bowed my wrists at the top, which has the effect of flattening the shaft and getting it more on plane in my downswing. I also delayed and reduced my lower body turn in the downswing.
I am not able yet to do all this at full speed, but the progress is encouraging.