Scaling laws for Large Language Models govern macroscopic resource allocation, yet translating them into precise Mixture-of-Experts (MoE) architectural configurations remains an open problem due to the combinatorially vast design space. This paper proposes a reusable framework for holistic MoE architectural optimization that addresses limitations in existing approaches. The authors demonstrate that FLOPs per token alone is insufficient for fair comparison of MoE models because varying computational densities across layer types can inflate parameters without proportional compute cost. They establish a joint constraint triad of FLOPs per token, active parameters, and total parameters, then reduce the 16-dimensional architectural search space to two sequential low-dimensional phases through algebraic constraints.