The game should absolutely be moved to a different weekend. Having the biggest rivalry game on campus on a weekend when the students are gone is absurd. Having the game the last week is only really exciting when one or both teams are playing to clinch something like a bowl game or divisional championship. Most years each team will have their bowl hopes determined already and the opportunity to clinch a divisional championship is decidedly rare for these teams. The only reason to keep the game the last weekend is "tradition," and tradition is not a good enough reason to exclude students - an important part of the tradition, rivalry, and fun of the game. Plenty of schools have rivalry games earlier in the year with great success. It may actually benefit this rivalry to be played when other rivalry games aren't as it might get a little more attention. Playing it in October, for example, during a week when there are no other big rivalry games and each team still has a winning or 500 record would likely be a much more exciting environment than the one witnessed this year. This game should be a sell-out on both campuses and neither school is likely to achieve that by holding it on the saturday after Thanksgiving. The Bucket Game with 30,000 non-students in attendance is really a shame and both schools should do what they can to rejuvenate interest, starting first with moving the game to a time of the year better suited to these programs, the fans, and the students.
I'm not a fan of moving the game to a neutral site, but I could live with it every third year.