@JHafer -
Just my observation, but it seems like you are in a contradiction - you want student to see the assignment, but the assignment should be in a module that you do not want students to see. I am confused as to why you would have that particular setup. I am not sure why (because of due date) the assignment has to be in a module as opposed to just in the assignments.
I am not sure, but you could try also adding the assignment in an earlier module - the time when students could actually see it and keep it in the other module as well. But I guess that defeats the statement of the assignment needs to be in the last module.
The only other option I could think of would be to put it in its own module - which again defeats the statement that it needs to be in the last module.