Some possible things to compete on, that could be automatically measured (with more or less dev work):
1 and 3 seem too easy to inflate, but 2 is a good idea. Instead of blocking specific websites, write a program that passively measures how much time you spend there, and compete with other people to get a low score. Maybe everyone puts some money in the prize fund...
Here's an internal dialogue I just had.
Q: How do we test rationality skills?
A: We haven't come up with a comprehensive test yet.
Q: Maybe we can test some part of rationality?
A: Sure. For example, you could test resistance to akrasia by making two contestants do some simple chores every day. The one who fails first, loses.
Q: That seems like a pointless competition. If I'm feeling competitive, why would I ever skip the chores and lose?
A: Whoa, wait. If competitiveness can cure akrasia, that's pretty cool!
Now we just need to figure out how to make people more competitive in the areas they care about...