Context. 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. Aims. 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. Methods. We performed spectral energy distribution fitting on archival broadband photometric continuum data from 1.2 to 850 μm 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. Results. 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 the literature, which show no discernible trends with luminosity, and have a mean p = -1.4 ± 0.4. However, our sub-sample, with a mean power law index of -1.1 ± 0.3, is slightly flatter than would be expected for spherical envelopes in free fall (p = -1.5). Conclusions. We attribute flattened density profiles for our eight sources to one or more of the following: ongoing accretion from their natal filaments, convolution of sources with neighbours or the larger filament, spherical averaging of asymmetric features (for example fragments), or inflation of the envelope by a moderate far-ultraviolet field. 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-mass protostars.