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The inner shaft with the spirals is a bit loose to the top hat due to clearances. Welding will very likely, pull the top hat to a side, or make a wobble. And pulling to side, changes when spark triggers, advancing on near side, retard on far side. The set screws as suggested and use of dial indicator can null out run out. On VR distributors, welding may result in magnetization, and that can mess with sensor signal. VR sensing is inaccurate enough in standard form. I use tab wheels with significantly increased diameter, and digital outputs for accurate timing reference. I found that blueprinting distributors helped, improving the sensing technology with optical tab sensing is far superior, and cost effective, with features not possible with VR.
You can say nonsense and that is OK. My wife points out your white Dart, on occasions when it is stalled at a busy intersections in M'boro. She looked at me and said you have given me cars to drive for over 40 years, they are not new, but I have never been stalled.