Model dependence in simulated responses to stratospheric aerosol injection (SAI) is a major uncertainty surrounding the potential implementation of this solar climate intervention strategy. We identify here large differences in the aerosol mass distributions between two recently produced climate model SAI large ensembles, despite using similar climate targets, with the goal of understanding the drivers of such differences. Using a hierarchy of recently produced simulations, we identify three main contributors including: 1) the rapid adjustment of clouds and rainfall to elevated levels of carbon dioxide, 2) the associated low-frequency dynamical responses in the Atlantic Meridional Overturning Circulation, and 3) the contrasts in future climate forcing scenarios. Each contribution also represents a potentially irreducible uncertainty over the likely timeframe of a potential SAI deployment if a 1.5C target is to be met and the results thus suggest the need for significant flexibility in the deployment of SAI if enacted.