100% of all iPhone lease members will want to get a new iPhone, Why not? they already paid for it.
so it's gonna be messy. Apple should've predicted this and start its production months before.
I don't think it is a matter of starting production sooner.
They know how many people are on the upgrade program, they could just start preorder for them in advance (maybe one day before other customers) to find out how many of them are willing to change the phone and gave them the ability to chose the model. I'm not talking about giving them shipping priority, but just be able to preorder