Hi Leon!
Have you tried rendering the Cinema4D project as a video instead of exporting it to Mocha or AE? If you did it and doesn´t work as well, maybe you can create a plane in Cinema 3D and put the texture of that video you want to put in (I don´t use Cinema4D but I have seen things like that in other 3D programs).
In case you render the project as a video, AE should open it with no problem and in it is easy to track, with motion tracking or the “camera tracking” effect (in “perspective” section of effects).
Hope I helped you!