Gamification at Work - How to Make Employees Submit Timesheet on Time ?

A couple of days back I was talking to a colleague who had also done the Gamification course on Coursera about applying some concepts learned from there to change the behavior at work. One of the most obvious behavior change we urgently require is to have everyone submit their Timesheet on time.

As a Consultancy, we earn money by charging our clients for the services we provide. The invoice cannot be created unless everyone on a project submits their timesheet. The invoice takes weeks to process adding a strain on the company finances. This whole process is jammed even if a single consultant misses submitting his timesheet.

Sadly, that conversation ended there hoping that one of us will get back with a concrete idea. But luckily we were not the only one brainstorming on this. Today I received an email that takes a new approach to tackle this issue. Here is the communication flyer of the approach -

This is such a brilliant idea. Few of the observations are -

1. Disciplinary approach doesn't work out in all scenarios. As an employee you are expected to submit timesheet on time, but I haven't seen it being effective. 
2. I know other organizations where these activities are tracked and matters at time of annual review. I think this sort of approach based on fear demotivates employees in long run. Dan Pink talks against this approach in his book Drive -
   Carrots & Sticks are so last Century. Drive says for 21st century work, we need to upgrade to autonomy, mastery and purpose.
3. An added monetary reward to all employees for submitting timesheet is going to be too costly.
4. An individual award to someone who has been very punctual about timesheet would create competition as well as won't have mass effect. Majority would loose motivation since reward is only for a handful of people.
5. This approach rather than making filling timesheet an individual activity, it makes it a group activity. 
6. Also it adds a purpose to the whole activity. A fund for doing social good would appeal to more individuals than a fund for employee outings.
7. Some people are more enthusiastic about the reward for social good. They will be able to champion the cause in their local group/project.
8. In the end, if this actually makes people more disciplined about submitting timesheet, there are manifold savings, a part of which management would be more than happy to share.

Thanks to everyone who came up with such a simple idea with so great potential. I would keep tabs to see if it actually changes the behavior and results in a positive outcome. Cheers.