Plant carbon transport is controlled by a multitude of parameters both internal and external to the sugar transporting phloem tissue. Sucrose transporter kinetics, conduit hydraulic resistance, and xylem water stress are all hypothesized to impact the amount of carbon delivered to sink tissues. However, the most important traits determining carbon export under drought are not well understood, especially for species with active molecular regulation of sucrose transport. This in turn limits our ability to assess species' resistances to phloem dysfunction under drought. Here, we use an integrated xylem-phloem-stomatal model to calculate leaf water potential from soil dryness, which is then used to determine gas exchange and phloem pressure gradients. We quantitatively compare the impacts of phloem loading kinetics, including feedbacks between loading and phloem pressure, phloem conduit resistances, and stomatal responses to water stress, on the total carbon export to sinks during drought. Regulating sucrose transporter kinetics which downregulates loading at high phloem pressures prevented runaway viscosity in the phloem sap and was the most important determinant of export rates under drought. In contrast to previous models, we found this feedback mechanism decoupled stomatal traits from phloem export efficiency during drought and increased the operational range of phloem hydraulic resistances.