This describes the issue with PRNGs based on a Linear Congruential Generator. The issues are resolved by using a Mersenne Twister instead, which is the standard PRNG used today basically everywhere.
A generator that itself is not recommended as it’s both very slow and fails many tests.
The xorshiro generators are much better.
At this point you can probably use ChaCha8 (ChaCha20 but with 8 rounds instead of 20) seeded from the system's crng and be fine in most cases. Xorshiro is fine is most cases but is obviously not statistically perfect.
Marsaglia vehemently disagreed with your remedy. (And imo he was eventually proven right - MT is a much less common default today than it was 15 years ago.)