I'd use one instance to seed the others. I'm pretty sure you can do this safely fairly easily.
- Even small changes in the state space cause fairly large changes downstream - if you can ensure they don't have exactly the same starting space (and no identical state prefix), I wouldn't worry about producing identical numbers. For instance, using just the values 1,2,3 to seed three threads would work fine - you don't even need to seed the entire space. Another advantage: by using clearly predictable seeds you can easily discredit the idea that you're cherry-picking any runs (assuming you're trying to demonstrate something).
- It's trivial to seed in a way that means the resultant "children" are highly un-correlated. Just iterate in a breadth-first fashion; i.e. if you want to seed N x 623 int values, don't seed 623 values sequentially, but pick the first N and distribute, then the next N etc. Even if there's some correlation between the seeder and the children, the correlation between the various children should be virtually non-existant - and that's all you care about.
- I'd prefer an algorithm that allows deterministic execution whenever possible, so depending on urandom is not attractive. This makes debugging easier.
- Finally, and obviously - test. These PRNG are fairly robust, but by all means eyeball the results and do a few correlation tests inspired by what you're simulating. Most problems should be obvious - either you've seeded badly and there are obvious repeating subsequences, you you've seeded well, and then the quality is dictated by the PRNG limitations.
- For final executions, after you're done testing, you can seed the first of 623 state values using urandom for peace of mind and/or the thread ID.