Recent work has demonstrated that imaging systems can be evaluated through the information content of their measurements alone, enabling application-agnostic optical design that avoids computational decoding challenges. Information-Driven Encoder Analysis Learning (IDEAL) was proposed to automate this process through gradient-based. In this work, we study IDEAL across diverse imaging systems and find that it suffers from high memory usage, long runtimes, and a potentially mismatched objective function due to end-to-end differentiability requirements. We introduce IDEAL with Interchanging Optimization (IDEAL-IO), a method that decouples density estimation from optical parameter optimization by alternating between fitting models to current measurements and updating optical parameters using fixed models for information estimation. This approach reduces runtime and memory usage by up to 6x while enabling more expressive density models that guide optimization toward superior designs. We validate our method on diffractive optics, lensless imaging, and snapshot 3D microscopy applications, establishing information-theoretic optimization as a practical, scalable strategy for real-world imaging system design.