I did check a couple of hover segments from the flight record that @Hands0n posted - those had no obvious oscillatory behavior comparable to what was visible during forward flight. I can post the details later if anyone is interested.
In regular flight, at moderate stick movements, so moderate horizontal speeds, the P4 flew without any obvious oscillation. I tend to fly "briskly" unless taking specific video photography. And a lot of that flight was being performed by a friend who is learning to fly, and so was slow to moderate speeds. When I took the controls and gave it a bit of a thrashing at speed in goth GPS and Sport modes it became apparent.
At full forward Pitch the oscillation would be immediately apparent. It was a calm still day and there was a slight wobble at hover, unusual for a Phantom and witnessed by almost all of the similarly affected on the forums.
I tried Left and Right Roll and there was no visible evidence of the oscillation. I'm not sure about Pitch backwards, don't recall.
On fast vertical descents the oscillation was very pronounced, even more than purely horizontal. It was a bad whether descending vertically in its own column of prop wash or while travelling forward (ie. 45 degree descent rate). All of those moves should be in the logfile that you have - as by then I'd fully realised something was wrong and was poking at it from all angles, so to speak
