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This paper presents models to estimate the structure of density and magneticfield strength in spheroidal condensations, from maps of their column densityand their polarization of magnetically aligned dust grains. The density modelis obtained by fitting a column density map with an embedded p = 2 Plummerspheroid of any aspect ratio and inclination. The magnetic properties are basedon the density model, on the Davis-Chandrasekhar-Fermi (DCF) model ofAlfv\'enic fluctuations, and on the Spheroid Flux Freezing (SFF) model of massand flux conservation in Paper I. The field strength model has the resolutionof the column density map, which is finer than the resolution of the DCFestimate of field strength. The models are applied to ALMA observations of theenvelope of the protostar BHR71 IRS1. Column density fits give the densitymodel, from (2.0 +- 0.4) x 10^5 cm^-3 to (7 +- 1) x 10^7 cm^-3 . The densitymodel predicts the field directions map, which fits the polarization map bestwithin 1100 au, with standard deviation of angle differences 17{\deg}. In thisregion the DCF mean field strength is 0.7 +- 0.2 mG and the envelope mass issupercritical, with ratio of mass to magnetic critical mass 1.5 +- 0.4. The SFFfield strength profile scales with the DCF field strength, from 60 x 10{\mu}Gto 4+-1 mG. The spatial resolution of the SFF field strength estimate is finerthan the DCF resolution by a factor ~7, and the peak SFF field strength exceedsthe DCF field strength by a factor ~5.

Magnetic Field Structure in Spheroidal Star-Forming Clouds. II. Estimating Field Structure from Observed Maps