The speed comes from running thousands of simulations in parallel on the GPU. The random number generator doesn't have to be any faster for this to be a huge speedup. It's possible to use any one you like. I did validate the one I'm using against various others and found equivalent results.
I also have the simulation implemented on the CPU as well to validate the correctness of the results.
Are you suggesting you compared the result using Math.random() on CPU to the accelerated hash functions from https://www.shadertoy.com/view/XlGcRh (linked from your source code comments)?
I believe that was one of the tests that I ran, yes. It was a long time ago. Obviously the results are not numerically identical when different RNGs are used but they converge as the number of iterations is increased. That said, I think you are right that the RNG could be improved, even if it doesn't affect the results right now.
I also have the simulation implemented on the CPU as well to validate the correctness of the results.