No, machining, not politics. If you want to center a hole in the end of a cylinder with a lathe, it is pretty easy: put it in the chuck, and make sure that you have it centered in the chuck using a dial indicator. Then use a center drill in the chuck in the tailstock, and voila! The hole will be centered within .010" or better without any effort at all.
In this case, I have a foot long piece of acetal, and it is both too heavy and too slippery for the Sherline chuck to hold it in position, even before you start the motor. I tried to locate the center hole using a micrometer by measuring the radius from several different points on the edge of the rod, and using where the micrometer scratches crossed, then used the drill press. This was close, but not quite close enough. Any other suggestions for how to do this?
UPDATE: Thanks for all the suggestions. I had forgotten the most obvious--measure multiple radii across the circle, and where they cross, is the center point. Using a right angle and then measuring the radii at a right angle from the two planes of the right angle should get it pretty accurate. Rotating the rod and repeating will minimize errors.