On some motors, the shaft sticks out the bottom by a mm or so. Check that it's not binding on the motor mount.
I can also confirm that this is not the issue sadly
I can confirm that the APM is realizing the quad is not stabilized, though it doesn't look like its making any effort to correct itself.
at 0-40% throttle the quad drops motor one by 15 - 30 degrees
at 41-60% throttle the quad is more or less stable
at 61-100% throttle the qaud drops motor one by 15-30 degrees again