  Astronomers have yet to establish whether high-mass protostars form from
high-mass prestellar cores, similar to their lower-mass counterparts, or from
lower-mass fragments at the heart of a pre-protostellar cluster undergoing
large-scale collapse. Part of the uncertainty is due to a shortage of envelope
structure data on protostars of a few tens of solar masses, where we expect to
see a transition from intermediate-mass star formation to the high-mass
process. We sought to derive the masses, luminosities, and envelope density
profiles for eight sources in Cygnus-X, whose mass estimates in the literature
placed them in the sampling gap. Combining these sources with similarly evolved
sources in the literature enabled us to perform a meta-analysis of protostellar
envelope parameters over six decades in source luminosity. We performed
spectral energy distribution (SED) fitting on archival broadband photometric
continuum data from 1.2 to 850 $\mu$m, to derive bolometric luminosities for
our eight sources plus initial mass and radius estimates for modelling density
and temperature profiles with the radiative transfer package Transphere. The
envelope masses, densities at 1000 AU, outer envelope radii, and density power
law indices as functions of bolometric luminosity all follow established trends
in the literature spanning six decades in luminosity. Most of our sources
occupy an intermediate to moderately high range of masses and luminosities,
which helps to more firmly establish the continuity between low- and high-mass
star formation mechanisms. Our density power law indices are consistent with
observed values in literature, which show no discernible trends with
luminosity. Finally, we show that the trends in all of the envelope parameters
for high-mass protostars are statistically indistinguishable from trends in the
same variables for low- and intermediate-mass protostars.
