Well that was easy. I took off the mounting ring, and the rear element was set in a metal cylinder that just screwed/unscrewed. So I hand tightened it. If I had a rubber grip of some sort, maybe I could have tightened it a bit more.
The rattle is gone and the lens is about as sharp at 2.8 as when it is stopped down to f8. It compares in sharpness to my Nikkor 80-200 f4 when I set that at 105mm. My tests were just visual, using my D200. Film tests may be more revealing, because of the resolution limitations of the D200's 10MP cropped image sensor. I'll take the lens for a spin next time I go out with my F100.
I may try later to tighten the rear element just a bit more but it seems pretty good right now. And for once, a 15 minute easy fix!