You need to use an armature. Constraint bone positions to empties. Those empties are children of your curve points (hooks).
You can only export deforming BONES.
An extensive series about this subject is here> https://youtu.be/hdGkKbtQxE0
I had this issue, turns out the Meshes I wanted to add more logic bricks were hidden in the 3d view port, which is why I wasn't able to add more logic bricks. Unhide your mesh within the 3d view-port, and you should be able to add more.