This work presents the Inverse-Optimized Pushover with Energy Redistribution (IOPER), a quasi-adaptive framework that reinterprets conventional static pushover analysis through cumulative hysteretic energy tracking. Instead of prescribing a fixed or modal-based lateral force pattern, IOPER embeds an externally scripted redistribution logic that penalizes overstressed regions and activates latent capacity zones, revealing alternative load paths and redundancy patterns essential for robust structural behavior. This enables a physically grounded evolution of the force vector without relying on internal adaptivity, making the method platform-agnostic, reproducible, and suitable for robustness-oriented assessment. The procedure unfolds in three stages: (i) an initial modal pushover used solely as an elastic baseline to quantify story-wise hysteretic energy demand; (ii) a second iteration where the lateral pattern is scaled to cumulative energy, capturing redistribution effects linked to structural memory; and (iii) a final capacity evaluation incorporating story-specific stiffness degradation coefficients. This sequence preserves interpretive clarity while emulating modal reshaping, softening, and progressive engagement phenomena typically observed in nonlinear dynamic response. IOPER is validated using two benchmark steel moment-resisting frames (9- and 20-story models), demonstrating improved drift distribution, enhanced curvature coherence, and closer alignment with NLTHA median envelopes compared to ASCE 41 static procedures and adaptive pushover procedures. Additionally, a full 3D steel frame is explored to illustrate how energy-governed redistribution reveals torsional participation, multi-directional degradation, and redundancy activation patterns that remain hidden in conventional force-based sequences. By reframing seismic demand as an energy narrative rather than a force prescription, IOPER offers a transparent and physically meaningful alternative for performance-based and robustness-oriented assessment. Its modular architecture, reproducibility, and natural extensibility to 3D systems position it as a promising tool for redistribution-sensitive design, fragility exploration, and nonlinear static validation workflows under uncertain or evolving seismic conditions.