In contrast to the canonical picture of transport by direct attachment to motor proteins, recent evidence shows that a number of intracellular "cargos" navigate the cytoplasm by hitchhiking on motor-driven "carrier" organelles. We describe a quantitative model of intracellular cargo transport via hitchhiking, examining the efficiency of hitchhiking initiation as a function of geometric and mechanical parameters. We focus specifically on the parameter regime relevant to the hitchhiking motion of peroxisome organelles in fungal hyphae. Our work predicts the dependence of transport initiation rates on the distribution of cytoskeletal tracks and carrier organelles, as well as the number, length, and flexibility of the linker proteins that mediate contact between the carrier and the hitchhiking cargo. Furthermore, we demonstrate that attaching organelles to microtubules can result in a substantial enhancement of the hitchhiking initiation rate in tubular geometries such as those found in fungal hyphae. This enhancement is expected to increase the overall transport rate of hitchhiking organelles and lead to greater efficiency in organelle dispersion. Our results leverage a quantitative physical model to highlight the importance of organelle encounter dynamics in noncanonical intracellular transport.