GPT-4 eventually got me to a place where I could quickly add constraints to the problem domain. Here’s my final objective function: 
Discussion
Using MiniZinc with GPT-4 was pleasant. I would try again with a more realistic example from daily life. If you want to see the full code, I did a longer write up: https://buttondown.email/aostiles/archive/flight-optimization-with-minizinc-and-gpt-4/