Then there's literally no point to using PRNG seeding. The whole point of PRNG seeding is so you can define some model in terms of "def model(inputs, state) ->" output, and get the "same" output for the same input. I put "same" in quotes because defining sameness on FP hardware is challenging. But usually 0.001% relative tolerance is sufficiently "same" to account for FP implementation weirdness.
If you can't do that, then your model is not a pure function, in which case setting the seed is pointless at best, and biasing/false sense of security in the worst case.
As you mention, non-pure models have their place, but reproducing their results is very challenging, and requires generating distributions with error bars - you essentially "zoom out" until you are a pure function again, with respect to aggregate statistics.
It does not sound like this model was "zoomed out" enough to provide adequate confidence intervals such that you could run the simulation, and statistically guarantee you'd get a result in-bounds.