Two new methods together increase the computational efficiency of the E3SM Atmosphere Model (EAM) version 2 (E3SMv2) over version 1 by a factor of approximately two in multiple configurations and on multiple platforms: first, high-order, property-preserving, remap-form, Interpolation Semi-Lagrangian (ISL) tracer transport; second, high-order, property-preserving physics-dynamics-grid remap. We describe extensions to these algorithms that together produce an extremely high-resolution tracer transport method coupled to a standard dynamics grid. In this method, the atmosphere has three point grids that share one element grid: the finite-volume physics grid with parameter n_f, the dynamics grid with Gauss-Lobatto-Legendre (GLL) basis parameter n_p^v, and the tracer transport grid with parameter n_p^t. We set n_p^v=4, as in all E3SM configurations, then increase n_f and n_p^t from their E3SMv2 values of, respectively, 2 and 4. Importantly for performance, the model time steps and number of communication rounds per unit of simulated time do not change. The GLL natural interpolant does not provide a stable Interpolation Semi-Lagrangian method for n_p^t ≥ 4. Thus, we describe new element-based, stabilized, high-order basis sets for the ISL method that are constructed to satisfy a stability criterion. We derive basis sets up to order of accuracy 9. Then we describe the property-preserving remap methods we use to transfer fields among the three point grids. Finally, we show results for a number of solution quality diagnostics on standard validation problems.