When you say Mersenne-Twister isn't good enough, what are the other shortcomings apart from speed? It seems that even modern versions of Python are continuing to use it...
Even a truncated 128-bit LCG has far better properties.
See https://www.pcg-random.org/index.html
The homepage might come across as a a little overzealous (for example ChaCha quality listed as good rather than excellent), but generally has good points.
They recommend to use their xoshiro PRNG.
https://www.reddit.com/r/programming/comments/8jbkgy/the_wra...
And the PCG author's response: https://www.pcg-random.org/posts/on-vignas-pcg-critique.html
For example, for one of his arguments, he specifically chose a generator called pcg32_once_insecure, which the PCG author does not recommend due to its invertible output function!
Personally, I have read both arguments in detail and I would always use PCG or even a truncated LCG over xoshiro, which has a large size in comparison, potentially worse statistical properties, and no gain- faster in some benchmarks and slower in others.
But I am using xoshiro in my projects, because I thought xor was simpler than multiplication.
But there exist some new and very fast PRNG's which are fast and extremely good. Almost TRNG, wyrand eg.