The sizes of three major or great historical earthquakes are reassessed using the isoseismal-area-regression tools developed in Parts I and II of this study of stable continental region (SCR) seismicity. The earthquakes are 1811 New Madrid, central United States, and its following sequence; 1886 Charleston, coastal South Carolina; and 1755 Lisbon, oceanic intraplate off the continental shelf of Portugal. The analysis confirms the large size of these events and for the first time places constraints on the uncertainty of their seismic moment release. Because of the exceptionally low seismic-wave attenuation of eastern North America (ENA), a separate North American regression of seismic moment on isoseismal area was developed. Additionally, the unknown western extents of the New Madrid isoseismal areas were calibrated with the patterns of the M 6.3-6.6 1843 and 1895 earthquakes. Application of Part II analysis procedures with these corrections yields New Madrid size estimates, expressed as moment magnitude, of M 8.1±0.31 for the 1811 December 16, M 7.8±0.33 for the 1812 January 23, and M 8.0±0.33 for the 1812 February 7 principal events. The Charleston earthquake's magnitude decreases from M≳7.4 to M 7.3±0.26 after compensation for the effect of coastal plain sediments on its inner isoseismals. Intensity regressions for Lisbon are calibrated against the isoseismal pattern of the nearly co-located M 7.8 1969 St Vincent earthquake, which in this case increases the predicted size of Lisbon from M 8.4 to M 8.7±0.39. These size estimates are supported by data from independent phenomena: extent and severity of liquefaction, the maximum distance of induced landslides, and for Lisbon, tsunami wave amplitudes. Estimated source parameters are controlled by crustal or lithospheric temperature, which governs the depth extent of brittle faulting. Using estimated continental and oceanic geotherms, viable fault lengths are 30–80 km for Charleston, 120–180 km for 1811 New Madrid, and 180–280 km for Lisbon for average displacements of 2–4 m, 8–11 m, and 10–14 m, respectively, and for average static stress and strain drops. At the estimated seismic moments of this study, the 1811 New Madrid and the 1755 Lisbon events are, respectively, the largest known SCR and oceanic lithosphere earthquakes.