That does sound like a horrible system. I know I sure wouldn't want to do any work if the grades were finalized and out.
What age group are you teaching? When I taught junior high in Japan, I put in place a reward system each term. I photocopied dollar bills with other teachers' faces, and passed them out for volunteering, speaking to me in English for several minutes, getting As on tests, doing writing assignments in their notebooks, etc. I had a whole system planned out with clear monetary rewards. At the end of the term, I then held an auction with magazines, T-shirts, and the like that I had picked up during vacation. It cost about $50 for everything, but those kids were motivated!!
Maybe you could try something similar, and hold an auction during those two weeks? You could post opening bids for certain items, and give students the chance to accumulate more money in those final days of the term.