Use the due date as a start date and tag the task as "deferred."
If you want to hide the task from a smart list, set the condition of the list to exclude tasks tagged as "deferred." I have task lists showing all available tasks, due/overdue tasks, and high priority tasks, all of which are set to hide tasks that are tagged "deferred."
This is so simple that I think I must be doing something wrong here. What am I missing?