A growing number of out-of-equilibrium systems have been created and investigated in chemical laboratories over the past decade. One way to achieve this is to create a reaction cycle, in which the forward reaction is driven by a chemical fuel and the backward reaction follows a different pathway. Such dissipative reaction networks are still relatively rare, however, and most non-enzymatic examples are based on the carbodiimide-driven generation of carboxylic acid anhydrides. In this work, we describe a dissipative reaction network that comprises the chemically fueled formation of phosphoramidates from natural ribonucleotides (e.g., GMP or AMP) and phosphoramidate hydrolysis as a mild backward reaction. Because the individual reactions are subject to a multitude of interconnected parameters, the software-assisted tool "Design of Experiments" (DoE) was a great asset for optimizing and understanding the network. One notable insight was the stark effect of the nucleophilic catalyst 1-ethylimidazole (EtIm) on the hydrolysis rate, which is reminiscent of the action of the histidine group in phosphoramidase enzymes (e.g., HINT1). We were also able to use the reaction cycle to generate transient self-assemblies, which were characterized by dynamic light scattering (DLS), confocal microscopy (CLSM), and cryogenic transmission electron microscopy (cryo-TEM). Because these compartments are based on prebiotically plausible building blocks, our findings may have relevance for origin-of-life scenarios.