This paper presents a Mixed-Initiative (MI) framework for addressing the problem of control authority transfer between a remote human operator and an AI agent when cooperatively controlling a mobile robot. Our Hierarchical Expert-guided Mixed-Initiative Control Switcher (HierEMICS) leverages information on the human operator's state and intent. The control switching policies are based on a criticality hierarchy. An experimental evaluation was conducted in a high-fidelity simulated disaster response and remote inspection scenario, comparing HierEMICS with a state-of-the-art Expert-guided Mixed-Initiative Control Switcher (EMICS) in the context of mobile robot navigation. Results suggest that HierEMICS reduces conflicts for control between the human and the AI agent, which is a fundamental challenge in both the MI control paradigm and also in the related shared control paradigm. Additionally, we provide statistically significant evidence of improved, navigational safety (i.e., fewer collisions), LOA switching efficiency, and conflict for control reduction.