Several searches have found evidence of $^{60}$Fe deposition, presumably from a near-Earth supernova (SN), with concentrations that vary in different locations on Earth. This paper examines various influences on the path of interstellar dust carrying $^{60}$Fe from a SN through the heliosphere, with the aim of estimating the final global distribution on the ocean floor. We study the influences of magnetic fields, angle of arrival, wind and ocean cycling of SN material on the concentrations at different locations. We find that the passage of SN material through the mesosphere/lower thermosphere (MLT) is the greatest influence on the final global distribution, with ocean cycling causing lesser alteration as the SN material sinks to the ocean floor. SN distance estimates in previous works that assumed a uniform distribution are a good approximation. Including the effects on surface distributions, we estimate a distance of $46^{+10}_{-6}$ pc for a $8-10 \ M_{\odot}$ SN progenitor. This is consistent with a SN occurring within the Tuc-Hor stellar group $\sim$2.8 Myr ago with SN material arriving on Earth $\sim$2.2 Myr ago. We note that the SN dust retains directional information to within $1^{\circ}$ through its arrival in the inner Solar System, so that SN debris deposition on inert bodies such as the Moon will be anisotropic, and thus could in principle be used to infer directional information. In particular, we predict that existing lunar samples should show measurable $^{60}$Fe differences.