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Modern accelerators use hierarchical parallel programming models that enable massive multithreading within a processing element (PE), with multiple PEs per device driven by traditional processes. Batching is a technique for exposing PE-level parallelism in algorithms that have traditionally run on MPI processes or multiple threads within a single process. Opportunities for batching arise in, for example, kinetic discretizations of magnetized plasmas where collisions are advanced in velocity space at each spatial point independently. This paper builds on previous work on a high-performance, fully nonlinear, Landau collision operator by batching the linear solver, as well as batching the spatial point problems and adding new support for multiple grids for multiscale, multi-species problems. An anisotropic relaxation verification test that agrees well with previous published results and analytical models is presented. The performance results from NVIDIA A100 and AMD MI250X nodes are presented with hardware utilization analysis for each architecture. The entire implicit Landau operator time advance is implemented in Kokkos for performance portability, running entirely on the device and is available in the PETSc numerical library.