7-day period is enough for the challenge, shorter period will be over challenging. Even with good posters, they totally depends on others users , including merit sources to received merits for their good posts. Other users, and merit sources, in turn have their own issues, some week they more actively log-in, and use the forum, read back and forth posts/ topics; some week they less actively use the forum than their usual levels.
The case becomes clearer if one user  mostly receive merits from local boards' merit sources. What will happen if merit sources turn into less actively in short period, less than 7 days?
Anyway, the new kind of challenge of the OP is interesting, and innovative. I don't see the exact rewards for winners mentioned in the OP, so can the OP clarify it more, please.