This paper analyzes and develops a multi-variable& multi-constraint design optimization approach with the goal of minimizing power losses in a 2 MHz LLC resonant converter for next-generation data center applications. For a thorough co-design of a multi-MHz resonant converter, intricately curated performance constraints and associated design-based trade-offs are presented. In addition, accurate characterization, and parametric minimization of the AC resistance by optimal selection of transformer winding configuration, while achieving a controllable leakage flux for the resonant inductor integration into the high frequency planar transformer (HFPT) thereby reducing the effective winding losses by 6%. An all-GaN based 700 W, high power density(6.2W/cm3) experimental proof-of-concept was built for a conversion from a variable input bus voltage (380-420 V) to 12 V stiff output at a resonant frequency of 2 MHz. The results portrayed a steady state peak efficiency of 95.65%, with an improvement of 2.2% over the state-of-the-art (SOA) operable at MHz frequency.