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How embedded, actively accreting low-mass protostars accrete their mass is still greatly debated. Observations are now piecing together the puzzle of embedded protostellar accretion, in particular with new facilities in the near-infrared. However, high-resolution theoretical models are still lacking, with a stark paucity of detailed simulations of these early phases. Here we present high-resolution non-ideal magneto-hydrodynamic simulations of a Solar mass protostar accreting at rates exceeding 10\(^{-6} M_{\odot}\) yr\(^{-1}\). We show the results of the accretion flow for four different protostellar magnetic fields, 10 G, 500 G, 1 kG, and 2 kG, combined with a disk magnetic field. For weaker (10 G and 500 G) protostar magnetic fields, accretion occurs via a turbulent boundary layer mode, with disk material impacting across the protostellar surface. In the 500 G model, the presence of a magnetically dominated outflow focuses the accretion towards the equator, slightly enhancing and ordering the accretion. For kG magnetic fields, the disk becomes truncated due to the protostellar dipole and exhibits magnetospheric accretion, with the 2 kG model having accretion bursts induced by the interchange instability. We present bolometric light curves for the models and find that they reproduce observations of Class I protostars from YSOVAR, with high bursts followed by an exponential decay possibly being a signature of instability-driven accretion. Finally, we present the filling fractions of accretion and find that 90\% of the mass is accreted in a surface area fraction of 10-20\%. These simulations will be extended in future work for a broader parameter space, with their high resolution and high temporal spacing able to explore a wide range of interesting protostellar physics.