From what I have been able to find it appears setting the nav mesh to Dynamic is necessary to rebuild navigation for movable objects. There is a large performance cost in doing so, so I would prefer to use the Dynamic Modifiers Only mode. Adding a NavModifier component to Blueprints which need to update navigation does not seem to work. The player does not need to stand on the platform while it is moving, but only at the end of an animation.
Any help would be greatly appreciated!