Large language models increasingly mediate decisions that turn on moral judgement, yet a growing body of evidence shows that their implicit preferences are not culturally neutral. Existing cultural alignment methods either require per-country preference data and fine-tuning budgets or assume white-box access to model internals that commercial APIs do not expose. In this work, we focus on this realistic black-box, public-data-only regime and observe that within-country sociodemographic disagreement, not consensus, is the primary steering signal. We introduce DISCA (Disagreement-Informed Steering for Cultural Alignment), an inference-time method that instantiates each country as a panel of World-Values-Survey-grounded persona agents and converts their disagreement into a bounded, loss-averse logit correction. Across 20 countries and 7 open-weight backbones (2B--70B), DISCA reduces cultural misalignment on MultiTP by 10--24% on the six backbones >=3.8B, and 2--7% on open-ended scenarios, without changing any weights. Our results suggest that inference-time calibration is a scalable alternative to fine-tuning for serving the long tail of global moral preferences.