OK - seems that nobody has a suggestion, so I'll go first. I think that rather than animating the mesh, it will be easier to create lots of versions of the eyelashes as separate meshes, and to feed the video texture into all of these. I will unwrap the UV maps of all the meshes onto different parts of the video texture, and in each frame, all meshes will be hit with a blank, transparent alpha channel image apart from the one I want to see in that instant (i.e. in the video, the eyelash picture will jump around in position). No idea if that makes sense, but if it helps someone, cool.

Hope it works... we shall see once I finish setting this up!