I just made a donut chuck. The chuck itself turns perfectly but once I attach something to it the work piece wobbles. I know it's because the piece isn't centered exactly. I've tried several times remounting with no luck.

Thinking back I don't recall anyone that made a video of how to build one of these things show an actual work piece mounted and spinning. They probably have the same problem.

It's good enough to remove what's left of the tenon, sand and apply a finish. But certainly not for final bottom shaping.