Thanks for the tips, guys.
Using my caliper to measure, it doesn't appear the screw is bottoming out the hole in the barrel block. I've seen a few guys on the CMP forum recommend a washer between the knob and the mount. This didn't appear to be what mine needs, but after looking at it harder, it's a possibility that the detent in the mount, that contacts the indentations in the back side of the knob, is bottoming out, not allowing the knob to fully tighten. I may try a thin washer here, with a section cut out to allow the detent to still contact the inside of the knob.
It was obvious that there was some vertical play in the mount, which is why I used a little shim to tighten it up. But after firing a few rounds, the movement appeared to be more horizontal than vertical- I may need to shim both surfaces. I just haven't messed with it yet.