If performance is not as critical, I would probably pick AES or Chacha any day over those. Furthermore they make parallelizable reproducible streams trivial.
A neat remark from the above: Monte-Carlo simulations run at the Los Alamos National Laboratory relied on a relatively simple linear congruential generator (LCG) producing 24- or 48-bits integers for at least 40 years
I suppose the question is do you really need to get rid of the Mersenne-Twister? Most of the modern variants are good enough for most practical purposes.