It sounds like noise could possibly be triggering your probe. Adding a capacitor across the input should help, if noise is the culprit.
I've never done any probing, but here's how I'd go about probing your turning.
Rather than probing the entire turning, which will take a considerable amount of time, I'd probe a single pass along the length of the turning, to get the profile. I'd then bring those probed points into a CAD program, draw a line through the points, and revolve it.
Then you'd have a model of your turning in your CAD program, to do whatever you want with.
Be aware that this will probably require writing your own probe routine, and figuring out some way to bring the points into your CAD programl. Then, you''ll need to figure out how to program whatever you want to do without having to go over the entire turned surface.
This will probably not be a trivial task. It would probably be much easier to just have the CNC do the entire turning from start to finish. But I'm sure that's not really what you want.