The basic design of Asana is that tasks assigned to a project appear in that project’s task list. Given this model, when a subtask is assigned to a project, it displays in the project’s task list. I don’t know this for a fact but I strongly suspect that the Asana folks concluded that automatically assigning all subtasks to their parent task’s project, thereby causing them all to appear in the project’s task list, would be too unwieldy and would be counterproductive.
I think the only solution would be for them to alter the basic design of Asana such that subtasks assigned to a project would not show in the project’s task list. Again I don’t know this but I suspect that given Asana’s architecture, it would be a heavy lift for them to make make that change. (Although interestingly it’s the design I’m implementing for my upcoming Desksana integration.)
You might be able to solve this using the "Add subtasks from a template" rule action in Flowsana. What I’m thinking is to assign the subtasks in the template to the “Production Schedule” project so that when they’re duplicated, they’ll be assigned to that project when they’re created. I don’t know if that matches your workflow without knowing more about it, but it might. The other issue is that the templated subtasks will show in that project, which you don’t really want, but perhaps since they won’t have any start or due dates on them, that wouldn’t be an unbearable issue.