In recent years, complex convolutional neural network architectures such as the Inception architecture have been shown to offer significant improvements over previous architectures in image classification. So far, little work has been done applying these architectures to music information retrieval tasks, with most models still relying on sequential neural network architectures. In this paper, we adapt the Inception architecture to the specific needs of harmonic music analysis and use it to create a model (InceptionKeyNet) for the task of key estimation. We then show that the resulting model can significantly outperform state-of-the-art single-task models when trained on the same datasets. Additionally, we evaluate a broad range of augmentation methods and find that extending augmentation policies to include a more diverse set of methods further improves accuracy. Finally, we train both the proposed and state-of-the-art single-task models on differently sized training datasets and different augmentation policies and compare the differences in generalization performance.