A multi-mode operation strategy, wherein an engine operates compression ignited at low load and spark-ignited at high load, is an attractive way to achieve better part-load efficiency in light duty, spark-ignition (SI) engines, while maintaining robust operation and control across the operating map. Given the sensitivity of compression ignition operation to in-cylinder conditions, one of the critical requirements in realizing such a strategy in practice is accurate control of intake charge conditions - pressure, temperature, as well as fuel loading, to achieve stable combustion and enable rapid mode-switches. A reliable way of characterizing fuels under such operating schemes is key. Towards this, this paper presents the second of a two-part study, comparing the reactivity trends for five, high octane gasolines in a modern SI engine operated in an advanced compression ignition mode to the behavior measured under similar thermodynamic conditions, but in the static environment of a rapid compression machine. In this work, a detailed chemical kinetic model is utilized with multi-component surrogates representing the full boiling-range gasolines to evaluate predicted autoignition behavior under the same scenario. While Shah et al. [1] demonstrated that the overall trends were found to be similar between the two experimental devices, when compared appropriately, this study finds that the model lacks adequate fidelity to properly distinguish chemical kinetic interactions between various fuel constituents. Important combustion metrics, including combustion timing and rates of heat release, are skewed. Additional work appears necessary in order to confidently apply kinetic models for multi-mode engine design / control, and fuel co-optimization.