Mooseman - I was just trying to use wording that had already been expressed. But yes, that is the relevant ruling and Shapeshifters will not get around the Dreadnaught.
Limited - The rule Mooseman stated handles both CIP and "as this comes into play" abilities. The example in the ruling should make it fairly clear.
Consider Spike Feeder. It comes into play with 2 counters. All of that is "as it comes into play" stuff. If Spike Feeder's ability were triggered, it would die as a state based effect.
In terms of the Dopelganger, CIP and "Comes into play" abilities only matter when it actually comes into play. I believe the change ability triggers at the beginning of upkeep, so if it changes, it is too late for a "beginning of upkeep" trigger for whatever you copied to also trigger. However, if whatever it is currently copying has a beginning of upkeep trigger, both it and the Dopelganger's change ability will be applied, even if you change to something else.