This study presents a multi-physics co-design framework addressing electromagnetic-thermal coupling challenges in radio frequency system-on-chip (RFSoC) modules for the 110 m QiTai radio Telescope (QTT). A hierarchical electromagnetic assessment methodology combining near-field scanning (2.4 ~ 40 GHz) and signature separation algorithms enables precise identification of nine dominant radiation sources at the component level, while board-level power loading analysis establishes a 70dB shielding effectiveness (SE) requirement for stable operation. The proposed electromagnetic-topology-optimized detachable shielding enclosure integrates nonlinear strain-compensated conductive elastomers (σ = 1.8 × 10³ S/m, εmax = 150%) and waveguide-embedded multi-mode optical interfaces (λ = 850/1310nm), achieving > 70dB SE with maintained optical communication integrity (BER < 10⁻¹²). Concurrent DELPHI-derived thermal network optimization results in a unified shielding-cooling architecture, reducing the maximum junction temperature from 84.1 °C to 40.0 ± 0.5 °C under 35 W/cm² power density through enhanced heat flux paths. Anechoic chamber measurements validate the frequency-dependent SE degradation mechanism of optical-fiber-embedded waveguides, confirming compliance with IEC 61000-4-21 Class A standards. The framework systematically resolves shielding-communication trade-offs and thermal accumulation constraints in high-density RFSoCs, providing a scalable paradigm for next-generation radio telescope electronics operating in extreme observational environments.