The Surface Water and Ocean Topography (SWOT) mission provides reservoir water surface elevation (WSE), but converting absolute WSE to storage remains sensitive to the relative reference and shape of hypsometric curves. Here, we evaluate a site-specific vertical alignment parameter and a hydrostatic-constrained extension for truncated hypsometric curves using 14 reservoirs with concurrent in-situ records and two hypsometric curves: GRDL (Global reservoir dataset through deep learning) and REGEOM (geometric approximation). Under the reference assumption that the maximum observed SWOT WSE corresponds to full capacity, the median capacity-normalized root mean square error (RMSE) is 14.9%. The reservoir-specific full-record calibration reduces this value to 2.9%, showing that effective vertical alignment is a major sensitivity. GRDL yields lower capacity-normalized RMSE than REGEOM. Artificial-truncation experiments show that the constrained extension reproduces withheld portions of tabulated curves with median reconstruction errors below 1% across the tested distances. A chronological 60/40 holdout test supports temporal generalization after local calibration: for the 11 reservoirs, the median capacity-normalized RMSE is 0.026 in both calibration and validation periods. In contrast, leave-one-reservoir-out tests find no statistically significant improvement over the reference assumption. The results therefore support locally calibrated, sampled storage retrieval while showing that transfer of a single alignment parameter to fully ungauged reservoirs remains unresolved.