Is it OK to reseed a Deterministic Random Bit Generator from itself?
No, in your situation (where you don't care about security), there isn't any harm in seeding the generator from its own output (or, for that matter, reseeding it by just incrementing the original seed, and resubmitting it).

The chief issue would be if you would fall into a loop (that is, you start repeating outputs); if the seed you generate is 128 bits or more, that is highly improbable for any reasonable number of reseeding.

Now, as you are well aware, a CSRNG is overkill for your purpose; however the question is whether it is cheap overkill.  If the total amount of time your simulation takes is short, or if the bulk of your computation is in things other than generating the random string (and so taking a bit longer in the generation part doesn't significantly slow you down), then it is cheap overkill.