I think if the flat earthers would be left completely "alone" with their experience, without anyone commenting/explaining anything there would be less resistance from their side. This is a "war" of perspectives in a sense and they are used to argue against the knowledge of physics and the traditional point of view. Putting an "opposition member" on the crew together with them and making them listen to what he says might ruin the impact of pure experience.
Instead, it would be better to keep the approach: "Do you want to see for yourselves? Come, we offer you a free flight to orbit". Instead of a documentary, it could be a reality show. The cameras would focus on their reactions/moods, the discussions amongst themselves, and how (and if) their opinions change as time passes. They could ask staff members anything they'd want to know, like how the rocket works, what are the distances, the speed, etc. But no one would educate them unless they asked.