We report the results of a high angular resolution near-infrared survey of dusty Wolf-Rayet stars using the Keck I Telescope, including new multiwavelength images of the pinwheel nebulae WR 98a, WR 104, and WR 112. Angular sizes were measured for an additional eight dusty Wolf-Rayet stars using aperture-masking interferometry, allowing us to probe characteristic sizes down to 620 mas (640 AU for typical sources). With angular sizes and specific fluxes, we can directly measure the wavelength-dependent surface brightness and size relations for our sample. We discovered tight correlations of these properties within our sample that could not be explained by simple spherically symmetric dust shells or even the more realistic "pinwheel nebula" (three-dimensional) radiative transfer model, when using Zubko's optical constants. While the tightly correlated surface brightness relations we uncovered offer compelling indirect evidence of a shared and distinctive dust shell geometry among our sample, long-baseline interferometers should target the marginally resolved objects in our sample in order to conclusively establish the presence or absence of the putative underlying colliding-wind binaries thought to produce the dust shells around WC Wolf-Rayet stars.