Just to reiterate - keyframe-driven Construction Script animations work absolutely fine in Sequencer when you’re viewing them in editor. You can animate the same way as you would do in After Effects, Blender or any other animation package.
But in order to export via the Movie Render Queue you have to pipe this animation into the Event Graph, as otherwise the Movie Render Queue doesn’t ‘see it’.
Previewing the Event Graph animation in editor (after ticking the option to ignore animations in Construction Script) works perfectly in my case - it’s doing exactly the same as it did via the Construction Script animation.
But once I hit the render button, something else happens. And I don’t understand why.