How to fix an independent group like a table?

I've tried using sticks and making the table non-independent, but this glues the torso in place, and I'd like it to slide around. I've also tried pinning but to no avail. I see that the relationship between the origin and the origin of the parent (the top level puppet in this case) does make a difference, but I still can't find a placement that completely stops the table from warping.
