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For next-generation neutrinoless double beta decay experiments, extremely low backgrounds are necessary. An understanding of in-situ cosmogenic backgrounds is critical to the design effort. In-situ cosmogenic backgrounds impose a depth requirement and especially impact the choice of host laboratory. Often, simulations are used to understand background effects, and these simulations can have large uncertainties. One way to characterize the systematic uncertainties is to compare unalike simulation programs. In this paper, a suite of neutron simulations with identical geometries and starting parameters have been performed with Geant4 and MCNP, using geometries relevant to the LEGEND-1000 experiment. This study is an important step in gauging the uncertainties of simulations-based estimates. To reduce project risks associated with simulation uncertainties, a novel alternative shield of methane-doped liquid argon is considered in this paper for LEGEND-1000, which could achieve large background reduction without requiring significant modification to the baseline design.