When reverberation chambers are loaded to increase the coherence bandwidth for modulated-signal measurements, a secondary effect is decreased spatial uniformity. We show that an appropriate choice of stirring sequence, consisting of a combination of mode-stirring mechanisms such as paddle and antenna-platform stirring, can mitigate the potential for increased uncertainty. We develop a new mode-stirring sample correlation model for uncertainty due to the stirring sequence. In a comparison with an empirical uncertainty analysis, the model is found to have an agreement within 2.5%. Our analysis is demonstrated for four loading cases in each of three reverberation chambers. The model is used to determine an optimal stirring sequence for a given chamber setup directly from correlations associated with each stirring mechanism. The model can also be understood in terms of the entropy of a measurement and it is shown that maximizing the entropy corresponds to a minimized uncertainty. The method presented here not only provides insight into sources of uncertainty but also allows users to determine an optimal mode-stirring sequence with minimized uncertainty for a given chamber setup.