There's a plugin for Kdenlive allowing a pixelated blur to follow an area of the video as it changes. Is there a way to do this with images or titles composited over the main video? I use Kdenlive for parody-style videos, and manually animating images over a moving target is a bit of a pain. Is what I described already possible?

You could do it with the Composite transition. The red rectangle can be moved around. You can then add keyframes.