One thing I have started doing lately, yes I know it's not the best use of tools but it works, is to take the bowl blank and a Forstner bit that is big enough to fit your chuck jaws into and expand to tighten, and drill a center hole in the blank. Just deep enough for the jaws.
If the blank isn't flat, like a natural edge blank would be curved, then I use the same bit and drill a flat ring around my center whole. That way the body of the chuck is closer to the wood. It allows the chuck to sit flat.
To do this I put the center point of the bit near the edge of the center whole. And just cut away enough material to make a flat surface around the center.
If it helps I would be happy to explain more tomorrow with pictures.
If I can add 1 more point to the worm screw, make sure the wood is firmly pulled into the jaws. It seems obvious but if the wood isn't flat all the way around the jaws, it will start to wobble around the screw when turning.