As poverty declines, the poverty line moves into the left tail of the conditional welfare distribution, where the parametric assumptions underlying the World Bank's small area estimation toolkit are most severely violated. I propose a three-layer methodology-Distributional Random Forests, BYM2 spatial smoothing, and optimal transport calibration-that estimates the full conditional distribution nonparametrically. Applied to Bolivia's 2024 Household Survey and concurrent Census (343 municipalities, 3.6 million households), the approach reveals a monotonic bias amplification: CensusEB's overestimation relative to DRF grows from 6% on the poverty headcount to 21% on the gap to 36% on severity. Against the direct survey, DRF's bias shrinks from 1.5 pp on FGT 0 to 0.7 pp on FGT 1 ; CensusEB's stays flat at 3.3-3.6 pp. The methods agree on who is poorest but increasingly disagree on how poor-and the disagreement grows monotonically with the taildependence of the measure.