Vacuum advance makes car shut off...WTF??

It might be worth checking the stops on the vacuum control. Perhaps they have been altered in a way, for too much travel.

There should be a clip to hold the plate down at the pivot point. Slop in the main shaft bushing, or wobble could be a problem too, exacerbated by the plate travel. There are also pads that support the plate. The grease can get sticky, resulting in bumpy travel.