> I'd ask you to check your basic assumption about science as an authority.
Science is the only and ultimate final authority. It really is not a bad assumption. There literally can not be a higher authority than it by definition.
> but is really bad at transmitting information about non-deterministic processes or even processes that are so complex that they appear non-deterministic e.g. human behavior.
No it is not, science functions perfectly fine for complex processes. We can describe and draw actionable conclusions from the behaviours of fluids and gases even though they are made up of inconceivably complex interactions of billions of quantum effects.
We could easily model most of human behaviour if we really wanted to. It is just that it is unethical to do so, so we refrain from it. We make do with observing humans in the wild, and the observations we make sometimes have enough significance to make weak statements about human behaviours.
If the belief in reincarnation could be used as a moral tool to help people think long term, that should be scientifically demonstrable if it's true. It would be a hard ethical argument though, as you're basically trading a persons ability to make correct judgements of their own safety and well-being for a larger "long term" better functioning society. Not saying it's definitely wrong, but it better lead to a much better world for it to be worth it.