Efficient coding of speech and audio in a distributed system requires that quantization errors across nodes are uncorrelated. Yet, with conventional methods at low bitrates, quantization levels become increasingly sparse, which does not correspond to the distribution of the input signal and, importantly, also reduces coding efficiency in a distributed system. We have recently proposed a distributed speech and audio codec design, which applies quantization in a randomized domain such that quantization errors are randomly rotated in the output domain. Similar to dithering, this ensures that quantization errors across nodes are uncorrelated and coding efficiency is retained. In this paper, we improve this approach by proposing faster randomization methods, with a computational complexity of $\mathcal O(N\log N)$ . The presented experiments demonstrate that the proposed randomizations yield uncorrelated signals, that perceptual quality is competitive, and that the complexity of the proposed methods is feasible for practical applications.