Also announced at the same conference was a way to make the output near-deterministic by submitting a fixed seed value. Did you try that?

Edit: I'm very confused why this is being downvoted. It's exactly what they advertised:

"Reproducible outputs and log probabilities

The new seed parameter enables reproducible outputs by making the model return consistent completions most of the time. This beta feature is useful for use cases such as replaying requests for debugging, writing more comprehensive unit tests, and generally having a higher degree of control over the model behavior. We at OpenAI have been using this feature internally for our own unit tests and have found it invaluable. We’re excited to see how developers will use it."

Yes, I noticed the seed/fingerprint caching announcement. Looks promising for all response types.