Calmcavok
Or, to turn it on its head:
With the AP disconnected, if you climb at 250kts, then fly level at 250kts, then desend at 250kts, you shouldn't need to trim as you trim for speed changes, not pitch.
That also wouldn't require much trim in a conventional flight control aircraft, such as a 747 or a 767. Maybe even some opposite trim:
From climb to level-off, the thrust reduction on the under-slung engines creates an exaggerated nose down moment, requiring nose up trim to maintain level flight and airspeed.
Likewise, a big thrust increase pushes the nose way up, requiring nose down trim to maintain speed in the climb.