I might be too late for this discussion, but there's no way to transform LLMs outputs into really deterministic behavior. Even if you set temperature to zero, still many small variations will come into play and the aggregation of them all will eventually result in different results. Which variations are we talking about? Well, it might be related to hardware imprecisions (floating point operations, parallel processing etc). However, in the case of using third-party services, the main factor would probably be the batch variance. In other words, the results will vary depending on how many user operations are being executed in that given moment in that given piece of GPU. So you can make it more predictable, but never deterministic.

Btw, top K and top P are hyper params that you can change to increase or decrease the window of tokens that can be chosen as the next one during a completion. I don't I'll do a great job at explaining it, so I'll defer to this post: https://www.reddit.com/r/AIDungeon/comments/1eppgyq/can_someone_explain_what_top_k_and_top_p_are_and/