Multilingual self-supervised learning (SSL) has often lagged behind state-of-the-art (SOTA) methods due to the expenses and complexity required to handle many languages. This further harms the reproducibility of SSL, which is already limited to few research groups due to its resource usage. We show that more powerful techniques can actually lead to more efficient pre-training, opening SSL to more research groups. We propose WavLabLM, which extends WavLM's joint prediction and denoising to 40k hours of data across 136 languages. To build WavLabLM, we devise a novel multi-stage pre-training method, designed to address the language imbalance of multilingual data. WavLabLM achieves comparable performance to XLS-R on ML-SUPERB with less than 10% of the training data, making SSL realizable with academic compute. We show that further efficiency can be achieved with a vanilla HuBERT Base model, which can maintain 94% of XLS-R's performance with only 3% of the data, 4 GPUs, and limited trials. We open-source all code and models in ESPnet.