We present coronal density profiles derived from low-frequency (80-240 MHz) imaging of three type III solar radio bursts observed at the limb by the Murchison Widefield Array (MWA). Each event is associated with a white light streamer at larger heights and is plausibly associated with thin extreme ultraviolet rays at lower heights. Assuming harmonic plasma emission, we find average electron densities of 1.8 x10^8 cm^-3 down to 0.20 x10^8 cm^-3 at heights of 1.3 to 1.9 solar radii. These values represent roughly 2.4-5.4x enhancements over canonical background levels and are comparable to the highest streamer densities obtained from data at other wavelengths. Assuming fundamental emission instead would increase the densities by a factor of 4. High densities inferred from type III source heights can be explained by assuming that the exciting electron beams travel along overdense fibers or by radio propagation effects that may cause a source to appear at a larger height than the true emission site. We review the arguments for both scenarios in light of recent results. We compare the extent of the quiescent corona to model predictions to estimate the impact of propagation effects, which we conclude can only partially explain the apparent density enhancements. Finally, we use the time- and frequency-varying source positions to estimate electron beam speeds of between 0.24 and 0.60 c.