This study constructs a fully data-driven and reproducible Southeast Asia Influence Index (SAII v3) to reduce bias from expert scoring and subjective weighting while mapping hierarchical power structures across the eleven ASEAN nations. We aggregate authoritative open-source indicators across four dimensions (economic, military, diplomatic, socio-technological) and apply a three-tiered standardization chain quantile-Box-Cox-min-max to mitigate outliers and skewness. Weights are obtained through equal-weight integration of Entropy Weighting Method (EWM), CRITIC, and PCA. Robustness is assessed via Kendall's tau, +/-20% weight perturbation, and 10,000 bootstrap iterations, with additional checks including +/-10% dimensional sensitivity and V2-V3 bump chart comparisons. Results show integrated weights: Economy 35-40%, Military 20-25%, Diplomacy about 20%, Socio-Technology about 15%. The regional landscape exhibits a one-strong, two-medium, three-stable, and multiple-weak pattern: Indonesia, Singapore, and Malaysia lead, while Thailand, the Philippines, and Vietnam form a mid-tier competitive band. V2 and V3 rankings are highly consistent (Kendall's tau = 0.818), though small mid-tier reorderings appear (Thailand and the Philippines rise, Vietnam falls), indicating that v3 is more sensitive to structural equilibrium. ASEAN-11 average sensitivity highlights military and socio-technological dimensions as having the largest marginal effects (+/-0.002). In conclusion, SAII v3 delivers algorithmic weighting and auditable reproducibility, reveals multidimensional drivers of influence in Southeast Asia, and provides actionable quantitative evidence for resource allocation and policy prioritization by regional governments and external partners.