You are going to make yourself crazy with that much homework!!
Think about that kid, what is something that might be important to him... game time, music, Mind Soccer and I would switch the scoreboard up. My scoreboard (I teach 7th grade) sometimes varies all week long. It is the few weeks so you don't need to do anything to wild, but maybe introduce a game like Mind Soccer and let them play to win time. My students love to play, and could play all the time! When I first introduced it I let them have a longer amount of time about 10 minutes, so they could really get into the game, then I made sure they ended on a tie. That way I could use that the following week as my scoreboard, I let them bank their time and played again on Friday- for at most 5 minutes! They were dying to break the tie!
About homework... last year about halfway through I quit giving "extra" homework, I only played to reduce their current assignment, it worked better for my class...
The Guff Counter is very powerful, but I think it has to be introduced at just the right time, you want to hold out as long as you can...
Let us know what you decide!