Maybe you should move up the deadline a week or so, and ask everyone to send them by then.
Then in the last week, you can get any stragglers, and wrap it up.
Everyone is busy. It's really hard to set a deadline, and then not expect people to follow it...I think with most things like this, everything gets sent in towards the very last moment.
You can send out mass PMs to everyone announcing the earlier date~ If people really want their letters included...they'll find time
