As new laser facilities are developed with intensities on the scale of ${10}^{22}\mbox{--}{10}^{24}\,{\rm{W}}\,{\mathrm{cm}}^{-2}$, it becomes ever more important to understand the effect of strong field quantum electrodynamic processes, such as quantum radiation reaction, which will play a dominant role in laser-plasma interactions at these intensities. Recent all-optical experiments, where GeV electrons from a laser wakefield accelerator encountered a counter-propagating laser pulse with a 0 > 10, have produced evidence of radiation reaction, but have not conclusively identified quantum effects nor their most suitable theoretical description. Here we show the number of collisions and the conditions required to accomplish this, based on a simulation campaign of radiation reaction experiments under realistic conditions. We conclude that while the critical energy of the photon spectrum distinguishes classical and quantum-corrected models, a better means of distinguishing the stochastic and deterministic quantum models is the change in the electron energy spread. This is robust against shot-to-shot fluctuations and the necessary laser intensity and electron beam energies are already available. For example, we show that so long as the electron energy spread is below 25%, collisions at a 0 = 10 with electron energies of $500\,\mathrm{MeV}$ could differentiate between different quantum models in under 30 shots, even with shot-to-shot variations at the 50% level.