The objective of this study is to evaluate and optimize an eco-friendly bioash–ground granulated blast furnace slag (GGBFS) binder for solidification/stabilization (S/S) of contaminated sandy–silt soil by identifying formulations that provide both mechanical strength and effective multi-element immobilization across curing time and carbonation aging. The soil contained elevated trace elements (As 403 mg/kg, Pb 806 mg/kg, Zn 398 mg/kg, Cu 526 mg/kg), exceeding Swedish guideline values for sensitive land use and requiring stabilization. A design-of-experiments (DoE) approach was used to define binder formulations. Mixtures were prepared at optimum moisture content (from Proctor compaction) and evaluated using unconfined compressive strength (UCS) testing and standardized batch leaching (SS-EN 12,457–2, L/S = 10). Leachates were analyzed for pH, electrical conductivity (EC), total organic carbon (TOC), inorganic carbon (IC), and dissolved trace elements. The dataset was analyzed using principal component analysis (PCA) and response-surface mapping to identify formulation regions that balance strength and leaching performance. Formulations (bioash 10–35%; GGBFS 5–15%) were cured for 28, 56, and 115 days. Carbonation aging was conducted for three weeks in sealed containers at laboratory temperature (19–24 °C) under CO₂ exposure. The formulation 35% bioash:15% GGBFS achieved the highest UCS (1438 ± 111 kPa at 56 days; n = 2) and strongly reduced leaching of cationic metals. Zn and Cd were below analytical limits (Zn < 2 µg/L; Cd < 0.05 µg/L), and Pb decreased by 99% relative to untreated soil. Arsenic leaching decreased by up to 43% after 28 and 115 days but increased transiently (20%) at 56 days. This increase coincided with CaCO₃ formation and lower-pH eluates with elevated Ca and IC, consistent with carbonation-driven changes in As retention. Compared with a cement-based binder, the bioash–GGBFS system moderated alkalinity while maintaining strength and improving Pb and As immobilization. Overall, the bioash–GGBFS system shows strong potential for sustainable remediation of metal-contaminated soils, although Cu and Ni require further optimization.