I know there have been very, very few rotations of the outer planets since they were discovered ... But would a single pass explain the change as first seen?
Once started, a “ripple” in Neptune’s orbit would continue all the way through the remaining passes of every orbit due to inertia. A satellite orbiting earth, for example, once bumped by a comet or second satellite or the Space Shuttle when it was serviced, will continue orbiting, but the sideways motion of that first bump would change each subsequent orbit.
ephemeris of neptune perturbed