Optimal reconstruction of a source sequence from multiple noisy traces corrupted by random insertions, deletions, and substitutions typically requires joint processing of all traces, leading to computational complexity that grows exponentially with the number of traces. In this work, we propose an iterative belief-combining procedure that computes symbol-wise a posteriori probabilities by propagating trace-wise inferences via message passing. We prove that, upon convergence, our method achieves the same reconstruction performance as joint maximum a posteriori estimation, while reducing the complexity to quadratic in the number of traces. This performance equivalence is validated using a real-world dataset of clustered short-strand DNA reads.