The weighted criteria is sort of a good idea in general that would be able to use as a hack for this specific problem. Having weighted criteria would be great for jams that want to focus on certain aspects but have other criteria also come into play. For jams like mine that have a small panel of judges, it could work as a hacky way of solving the rules violation since the judges can easily come to an understanding about the rules and can be trusted to use it responsibly. It could be a disaster if this hack is used in community voted jams though. Yet weighted criteria in general is a good idea I think.
The ideal would be exactly what No Time suggested. A back bin of games that are excluded from the main ranking. Those games could still recieve scores, but they wouldn't appear in the main ranking list, or separated out at the bottom of it. Someone could choose to put their game there when they submit it, and the jam host can also choose to move games there as well.
melerski, the reason it's problematic to me to have them mixed in is that people who come to play the games in the jam will expect that the games they play, especially the highly ranked ones, will conform to the rules. Taking my jam as an example, there are plenty of people who love adventure games but don't necessarily care for other genres of games. They may well come play the games entered into this jam as a way to discover new adventure game creators. If there are platformers and shooters and all manner of other types of games mixed in, those people will start losing faith in the games and the ranking as it offers them up games that aren't even in the right genre.
I have yet to see how big of a problem this will be (or even if it will be a problem) in my jam, but it's something I should be prepared for.