When making an animated matte over material with pulldown, you can't simply set a couple keyframes and let it go.  The matte will move on every field, while the image moves every other or third field, creating a jittery effect.  My solution has been to add keyframes and copy/paste to get the animation to hold while the image is holding.  This is very tedious, since it means keyframing almost half of the fields in the clip. 

Does anyone know of a better way to do this without going outside of Composer?

It would be great if effects that had animated position parameters would have something like an overall "Interpolation" parameter with an option to detect the pulldown sequence and apply it to the movement between keyframes.

If you are working with 3:2 pulldown material digitized in a 29.97 project, the workaround would have been to digitze the footage in a 23.976 project, and pulldown would have been removed. Not as easy if you're dealing with imported material.

You can try using the Timewarp effect to remove pulldown.  Search the help for "Timewarp: Pulldown Removal".  You could try rendering this effect and then doing the Animatte on top of that.  (You might need to mixdown as an intermediate step.)

Otherwise, even though it's a pain, After Effects is the way to go.  Animatte is great for simple fixes, but anything too complicated, and I jump over to AE.

HTH