Implement gamification on Time reporting to minimize late reports?

A company is having trouble getting its employees to report time of their working hours. The time reporting is the source for invoicing the company's customers and it has to be done in time. To deal with late time reports, the company implemented an unsatisfying wall where the most late employees are present on the companies wall board together with the number of hours late.

This current system is something like a reversed high score list, which is far from motivating. As expected, there are always employees on this list and it is never empty.

mockup

download bmml source – Wireframes created with Balsamiq Mockups

Instead of the current method that relies on negative feedback, my idea is to do the opposite: implement gamification elements, where you get points for days the reports are registered correctly. On display would be a high score list with the one first to finish current day and all preceding days.

mockup

download bmml source

I'm also thinking of implementing badges for consecutive reports on time, helping a colleague report on time, edits and making copies, report expenses correct and on time and a few more. This would be more satisfying for the employer and lessen the stress of avoiding a hall of shame.

Question: Would this be enough to get rid of late time reports, or is there more that could be done? Any other feedback on this idea is also appreciated.


Related:
How does Gamification change User Behavior?
How can you make a user experience addictive?