It has been a long time since I flew a PA38, but I think that the rudder blanking the horizontal stab/elevator is a reasonable explanation.
In normal flight the stab/elevator is providing a downward force (nose-up pitching moment), with the most critical airflow being the underside. If the rudder interferes with that there will be a pitchover effect.
The aircraft I've flown most affected by this was a military PC9, which would give about a -0.5 g pushover if you put full rudder in at about 100K. That opened your eyes if you weren't ready for it!
Just my guess.