  In the first paper in this series, we introduced "persistent gravitational
wave observables" as a framework for generalizing the gravitational wave memory
effect. These observables are nonlocal in time and nonzero in the presence of
gravitational radiation. We defined three specific examples of persistent
observables: a generalization of geodesic deviation that allowed for arbitrary
acceleration, a holonomy observable involving a closed curve, and an observable
that can be measured using a spinning test particle. For linearized plane
waves, we showed that our observables could be determined just from one, two,
and three time integrals of the Riemann tensor along a central worldline, when
the observers follow geodesics. In this paper, we compute these three
persistent observables in nonlinear plane wave spacetimes, and we find that the
fully nonlinear observables contain effects that differ qualitatively from the
effects present in the observables at linear order. Many parts of these
observables can be determined from two functions, the transverse Jacobi
propagators, and their derivatives (for geodesic observers). These functions,
at linear order in the spacetime curvature, reduce to the one, two, and three
time integrals of the Riemann tensor mentioned above.
