Did you try applying sklearn's PCA to a subsampled dataset? Randomly sampling 1% of your dataset would probably allow you to find the first four principle compo

Did you try applying sklearn's PCA to a subsampled dataset? Randomly sampling 1% of your dataset would probably allow you to find the first four principle components in less than 30 minutes. It would be interesting to see whether these components are significantly different to the ones you got on the whole dataset.