The forum image upload seems to be broken since the last update of the forum module. I hope this will be fixed soon. In the meantime, please upload the images in a third-party web service (SkyDrive, imageshack, etc.). I apologize for the inconvenience.
Since I do not know the exact bone configuration, movement ranges for the bone, etc. it is hard for me to give a concrete answer. Here is some general advice that might help:
If you use the ragdoll approach, then you cannot move the bone directly because this will violate the FixedJoint constraints. You have to either work with bones and without physics, or work with a ragdoll, physics constraints, ragdoll motors and do not move bones directly:
Approach A - Animation and IK only
Depending on the bone constellation it might be possible to achieve what you need with only the animation IK solvers. Maybe you can use the CcdIkSolver to move the platforms together. You can specify a callback method in the CcdIkSolver in which you can control the rotations of the bones, e.g. the rotation of the platforms.
Approach B - Physics only
Create a ragdoll and animate this ragdoll using ragdoll motors (similar to the ActiveRagdollSample in the CharacteraAnimationSample project). Use a FixedJoint to keep the platforms connected. Use a QuaternionMotor to control the orientation of the platform (instead of the LookAt constraint).
Both approaches might need careful tweaking to avoid instabilities. Ideally we could avoid both approaches and find an analytical solution for the problem. I haven't fully understood the problem description - maybe I am overlooking a much simpler solution.