Some basic tests: have you indicated the chuck body?
Chuck up a piece of cold rolled or centre-less ground stock, at the centre of rotation, and than make an improvised balance stand. you can easily get a feel for how unbalanced the chuck casting is. Your 4 jaws won't be more than a couple of grams off from each other, so there wouldn't be any worries about them.
Of the dozens of 4J chucks I've used this is an anomaly. If you prove that the chuck is balanced this way, you can begin to look for other sources of vibration. I'm worried that your headstock is bent. Now that I have seen.