Industrial starch extraction from cassava (Manihot esculenta Crantz) generates over 30 million metric tons of wet peel waste annually, presenting severe localized ecological hazards through anaerobic methane release and phytotoxic cyanogenic leaching. To promote engineering for sustainable development and bridge materials technology with food science, this study presents a computational and process-modeling empirical evaluation of a four-stage sequential cascade biorefinery designed for near-zero-waste valorisation. The process design leverages non-steady-state Fickian diffusion kinetics and Hansen Solubility Parameters to selectively isolate bioactive polyphenols, gelatinized starch, and hemicellulose/pectic oligomers before deconstructing the remaining cellular matrix into structural biopolymers. A three-factor Central Composite Design (CCD) optimized cellulose nanocrystal (CNC) extraction, validated by a simulated Analysis of Variance (SIMULATED ANOVA) multi-variable engine. Structural performance was evaluated by deriving explicit weak-form Galerkin finite element steps for an orthotropic bio-composite thin film under tensile configurations. The process model predictions demonstrate a progressive transformation of the biomass matrix, driving the cellulose Crystallinity Index (CrI) from a raw baseline of 32.4% to 81.6% in the purified CNCs, which enhanced composite tensile strength from 4.2 to 28.5 MPa. Techno-economic analysis (TEA) for a scaled 10 metric tons/day facility projected a Total Capital Investment (TCI) of $2,058,812.50 and a highly viable 20-year Net Present Value (NPV). Furthermore, ISO 14040/44-compliant cradle-to-gate Life Cycle Assessment (LCA) revealed a 55.3% reduction in global warming potential (1,272.20 kg CO2-eq) compared to conventional stockpiling baselines. This computational approach provides a rigorous process-engineering framework that successfully upcycles low-value agricultural discards into high-performance functional barriers for sustainable food packaging systems.