Automatic modulation classification is an important component in many modern aeronautical communication systems to achieve efficient spectrum usage in congested wireless environments and other communications systems applications. In recent years, numerous convolutional deep learning architectures have been proposed for automatically classifying the modulation used on observed signal bursts. However, a comprehensive analysis of these differing architectures and the importance of each design element has not been carried out. Thus, it is unclear what trade-offs the differing designs of these convolutional neural networks might have. In this research, we investigate numerous architectures for automatic modulation classification and perform a comprehensive ablation study to investigate the impacts of varying hyperparameters and design elements on automatic modulation classification accuracy. We show that a new state-of-the-art accuracy can be achieved using a subset of the studied design elements, particularly as applied to modulation classification over intercepted bursts of varying time duration. In particular, we show that a combination of dilated convolutions, statistics pooling, and squeeze-and-excitation units results in the strongest performing classifier achieving 98.9% peak accuracy and 63.7% overall accuracy on the RadioML 2018.01A dataset. We further investigate this best performer according to various other criteria, including short signal bursts of varying length, common misclassifications, and performance across differing modulation categories and modes.