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