Flywheel Energy Storage Systems (FESS) are used for high-power energy storage in applications ranging from grid stabilization to uninterruptible power supply, offering fast response and long cycle life. Stress constrained topology optimization of energy storage rotor designs using specific energy maximization offers a physically meaningful alternative to volume-constrained formulations, but challenges remain in achieving convergence and fully discrete designs. Previous work [1, 2] enabled stress-constrained designs, but the specific energy formulation was difficult to converge, and incorporating local stress constraints posed additional challenges, often resulting in gray regions and limited discreteness. This contribution presents a topology optimization framework to improve convergence and discreteness under a specific energy objective. Inspired by robust design approaches employing multiple projected realizations of the topology [3], the method evaluates the objective and constraints on carefully chosen projections, while periodically updating stress limits. The framework is implemented in a general SIMP-based topology optimization setting with density filtering, projection, and adjoint sensitivities. The approach is demonstrated on representative rotor design problems, showing faster convergence, higher discreteness, and reliable satisfaction of stress constraints compared to conventional formulations. Parametric studies indicate that the resulting designs are sensitive to numerical and design parameters such as density filter radius, rotor height, and operating speed, with two distinct families emerging: nearly axisymmetric shape-like profiles and spoke-based topologies. Comparisons with conventional shape optimization highlight that similar optimal performance can be achieved, emphasizing trade-offs between manufacturing complexity and geometric freedom. Overall, the framework, implemented in OpenFCST [4] based on the deal.II [5] finite element libraries, provides an efficient and flexible approach for stress-constrained specific energy optimization, supporting practical large-scale topology design.