Thank you for your response Fr_Chuck.
I'll try the "my answer is my answer" approach. Let's see what happens there.
I'm also going to let the timesheet lapser go this month until it's time to get paid; then let them know that they missed the deadlines. They might try sneaking all their weekly timesheets in to me before the end of the month though so they can get paid. Not sure what I can do at that point other than giving them a firm reminder that they need to be in weekly.