Recent advances in the development of large, programmable quantum simulation platforms based on Rydberg atom arrays has enabled the exploration of non-equilibrium dynamics in quantum spin models with power-law decaying interactions. In this talk, we outline an approach to simulate transport phenomena in two-dimensional spin networks, starting with the ballistic transport of single-spin excitations of a one-dimensional spin chain. We first validate the performance of a perturbative model driving spin transport, identifying the set of physical parameters maximizing the transport probability under realistic experimental conditions. We then quantify the performance of this approach to distribute entanglement among two distant qubits, benchmarking our results against two protocols based on mediating two-qubit gates and spatial displacement operations. To further quantify the detrimental effect of spin-motion entanglement on transport fidelity, we introduce and numerically characterize a dephasing channel acting on the internal spin state. This dephasing channel facilitates classical modeling of quantum dynamics on a classical computer, e.g., as needed to synthesize robust optimal control pulses. Towards experimental realization of the spin-transport protocols, we introduce the workflow and architecture of a low-latency feedback control system, which interfaces cameras, processors, and arbitrary waveform generators using a cost-efficient computer architecture. The first instance of this system enables optimizing the trap array parameters in a closed loop, including their geometry and trap depth uniformity. The second instance of this system enables solving atom reconfiguration problems, as needed to prepare defect-free configurations of atoms and engineer systems with dynamic connectivity by displacing atoms in space. We characterize the performance of this system, providing a detailed breakdown of the runtime data and discussing timing bottlenecks. These results support the development of an integrated platform for quantum simulation of spin-model dynamics in regimes inaccessible to classical modeling tools.