The construction of 10 PW class laser facilities with unprecedented intensities has emphasized the need for a thorough understanding of the radiation reaction process. We describe simulations for a recent all-optical colliding pulse experiment, where a GeV scale electron bunch produced by a laser wakefield accelerator interacted with a counter-propagating laser pulse. In the rest frame of the electron bunch, the electric field of the laser pulse is increased by several orders of magnitude, approaching the Schwinger field and leading to substantial variation from the classical Landau-Lifshitz model. Our simulations show how the final electron and photon spectra may allow us to differentiate between stochastic and semi-classical models of radiation reaction, even when there is significant shot-to-shot variation in the experimental parameters. In particular, constraints are placed on the maximum energy spread and shot-to-shot variation permissible if a stochastic model is to be proven with confidence.