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Runaway electron acceleration is the keystone process responsible for the production of energetic radiation by lightning and thunderstorms. In the laboratory, it remains undetermined if runaway electrons are merely a consequence of high electric fields produced at the ionization fronts of electrical discharges, or if they impact the discharge formation and propagation. In this work, we simulate photon pileup in a detector next to a spark gap. We compare laboratory measurements to ensembles of monoenergetic electron beam simulations performed with Geant4 (using the Monte Carlo method). First, we describe the x-ray emission properties of monoenergetic beams with initial energies in the 20 to 75 keV range. Second, we introduce a series of techniques to combine monoenergetic beams to produce general-shape electron energy spectra. Third, we proceed to attempt to fit the experimental data collected in the laboratory, and to discuss the ambiguities created by photon pileup and how it constrains the amount of information that can be inferred from the measurements. We show that pileup ambiguities arise from the fact that every single monoenergetic electron beam produces photon deposited energy spectra of similar qualitative shape and that increasing the electron count in any beam has the same qualitative effect of shifting the peak of the deposited energy spectrum toward higher energies. The best agreement between simulations and measurements yields a mean average error of 8.6% and a R-squared value of 0.74.