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This paper concludes a three-Part series on the limits the laws of physics place on the sustained performance of reversible computers. Part I concerned aggregate performance in terms of computational operations per unit time, but neglected to consider interactions among computational sub-units or between computational sub-units and shared resources such as memory or chemical species. Part II extended the analysis to consider the former set of interactions. In this Part we extend the analysis to consider the latter set, with a particular focus on resource distribution in the first half. It is found that most schemes imaginable fail to function effectively in the limit of vanishing 'computational bias' $b$, which measures the net fraction of transitions which are successful, and falls as the system grows in size. Driving thermodynamically unfavourable reactions, such as resource distribution, is a very general problem for such systems and can be solved by supplying a sufficient excess of free energy. We propose a scheme to dynamically supply enough free energy for a given reaction, automatically and rapidly adapting to changes in the disequilibrium state of said reaction--including the case when the favourable reaction direction switches. The overhead of this scheme is no worse than the overhead found in Part II for communicating reversible computers under the same regime.