One solution is to try and convince people to downvote more aggressively.

A second solution, which is one of my current research projects, is to develop a more effective automatic moderation mechanism than screening out low karma posts. If there is enough interest, it may be worthwhile to discuss exactly what the community would like automatic moderation to accomplish and the feasibility of modifying it to meet those goals (preferably in a way that remains compatible with the current karma system). Depending on the outcome, I may be interested in helping with such an effort (and there is a chance I could get some funding to work on it, as an application of the theory).

Another solution is to change the karma system to remove the psychological obstacles that may keep people from downvoting. It feels a little mean to directly cause a comment to be filtered, even when it would probably improve the mean quality of discourse. It may be a little easier to express your opinion that a comment is not constructive, and have a less direct mechanism responsible for converting a consensus into moderation / karma penalty.