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Machine learning (ML) models are becoming increasingly common in the atmospheric science community with a wide range of applications. To enable users to understand what an ML model has learned, ML explainability has become a field of active research. In Part I of this two-part study, we described several explainability methods and demonstrated that feature rankings from different methods can substantially disagree with each other. It is unclear, though, whether the disagreement is overinflated due to some methods being less faithful in assigning importance. Herein, "faithfulness" or "fidelity" refer to the correspondence between the assigned feature importance and the contribution of the feature to model performance. In the present study, we evaluate the faithfulness of feature ranking methods using multiple methods. Given the sensitivity of explanation methods to feature correlations, we also quantify how much explainability faithfulness improves after correlated features are limited. Before dimensionality reduction, the feature relevance methods [e.g., SHAP, LIME, ALE variance, and logistic regression (LR) coefficients] were generally more faithful than the permutation importance methods due to the negative impact of correlated features. Once correlated features were reduced, traditional permutation importance became the most faithful method. In addition, the ranking uncertainty (i.e., the spread in rank assigned to a feature by the different ranking methods) was reduced by a factor of 2-10, and excluding less faithful feature ranking methods reduces it further. This study is one of the first to quantify the improvement in explainability from limiting correlated features and knowing the relative fidelity of different explainability methods.