Synthetic tabular data lets organisations share, rebalance, and stress-test sensitive in-house tables-but only if the result is actually fit for the downstream task. Yet a table that matches the real distribution on aggregate statistics can still be unfit for its downstream task: it loses the rare cases that matter, is not optimised for the end task, and silently breaks the deterministic relations that domain data must obey. We present TabAutoSyn, an end-to-end, generator-agnostic pipeline that turns any base generator into deployment-ready synthetic data through four automated stages: generate, verify, augment, and curate. A multi-agent LLM module discovers functional dependencies and domain constraints from the real table and repairs or removes violating rows; a divergence-minimising stage rebuilds under-represented tails; and a curation stage provably never lowers a chosen downstream score. Across 22 public and proprietary datasets and eleven generators spanning five model families (GAN, VAE, diffusion, language-model, and graph), TabAutoSyn delivers the best train-on-synthetic utility and the highest validity while preserving privacy. Because it is generator-agnostic, it attains these results on a commodity GPU at a fraction of the cost of the strongest LLM-based baselines, and it needs no per-dataset tuning-making it practical to run on sensitive, in-house data.