I posted this problem on another that site (that will remain nameless) and someone finally suggested a solution that worked.

I simply opened a blank project and imported the problem project into it. When I applied filters, the same mysterious green bar appeared for ten seconds on either side of the affected clip, but the clip played fine. And no project before or since has had this problem.

So, to anyone else who has this problem: Try importing your project into a blank project, or into a project you know to be fine.

Thanks, everyone, for your help.