Area-dependent memristive devices based on the valence change mechanism are promising candidates for emerging analog and neuromorphic computing due to their intrinsic analog switching behavior and reduced variability. Among these, IGZO-based devices are particularly attractive owing to their potential for multifunctional applications, including optoelectronics and flexible electronics. However, systematic design strategies that directly link the material and interface properties to their device performance remain unexplored. In this work, we demonstrate that the switching polarity and electrical characteristics of IGZO-based memristive devices can be systematically tuned by modifying the top electrode. This control is shown to originate from changes in the band alignment and the resulting spatial electric field distribution across the device. To identify the governing interface and underlying transport mechanisms, we combine energy band diagram simulations with XPS-based band alignment measurements. Using this experimentally validated framework, the measured I-V characteristics are quantitatively reproduced within the Tsu-Esaki tunneling model. These results establish a consistent physical understanding of switching in IGZO-based devices and demonstrate that band engineering provides a powerful route to control both transport and switching behavior, enabling targeted optimization for large-scale analog and neuromorphic systems.