Because the mathematical analysis of time domain integral equations is fraught with difficulty, researchers are often forced to use experimental means to characterize the stability of their approaches. The difficulty inherent in this approach is that the variables affecting the success or failure of an experiment necessarily depend on a computer implementation of potentially hundreds of thousands of lines of instructions hiding unknown assumptions and even errors. In this work, the importance of different integration orders for near and far basis functions is investigated, and demonstrated to have an enormous effect on the stability of the implementation. Methods previously thought unstable for difficult problems are shown reliable with tiny changes over broad choices of parameter values.