We present a computational optimization framework for REBCO high-temperature superconducting coils combining electromagnetic-thermal-mechanical modeling validated through COMSOL Multiphysics and FEniCSx finite element analysis. The approach demonstrates systematic scaling from precision baseline configurations (2.1 T, 0.01% ripple) to high-field operation (7.07 T, 0.16% ripple) through multi-objective parameter optimization. Computational results project multi-tape conductor designs achieving 30% current utilization, thermal margins of 74.5 K, and mechanical reinforcement strategies reducing stress from 179 MPa to 35 MPa. Cross-platform FEA validation shows < 1% solver variance for electromagnetic and stress analysis. All results represent computational projections requiring experimental validation.