In this paper, we propose several novel data augmentation methods for improving the performance of automatic speech recognition (ASR) in low-resource settings. Using a 100-hour subset of English LibriSpeech to simulate a low-resource setting, we compare the well-known SpecAugment approach to these new methods, along with several other competitive baselines. We then apply the most promising combinations of models and augmentation methods to three genuinely under-resourced languages using the 40-hour Gujarati, Tamil, Telugu datasets from the 2021 Interspeech Low Resource Automatic Speech Recognition Challenge for Indian Languages. Our data augmentation approaches, coupled with state-of-the-art acoustic model architectures and language models, yield reductions in word error rate over SpecAugment and other competitive baselines for the LibriSpeech-100 dataset, showing a particular advantage over prior models for the ``other'', more challenging, dev and test sets. Extending this work to the low-resource Indian languages, we see large improvements over the baseline models and results comparable to large multilingual models.