Use blend shapes. Add a blend key, apply the displace modifier, that should work. Other than that, blender does not export the information you're looking for. Although it might be possible with the new alembic support? I am not entirely sure. My recommendation would be to do it with blend shapes though, and actually hook those blend shapes up to bones via drivers. That'd be the proper way to do it.
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or what else would you bake it to?