I really think the mechanic has lots of potential and deserves to be explored further. But I also think that you should probably ditch the physics based system (seems like it's based on some kind of rigidbody/joints system) and instead have a custom solution that handles the upper body and then updates the bones with something like a inverse kinematics system.
yeah, you are spot on, mu current solution relies on rigidbodies, which are impossible to control.
I think I would make it more 'tile-based' if that makes sense. Like, when you get a bone, you become 1 block taller, and extend 1 block further. I think that would work nicely for a puzzle game, but I'm ganna have to do some testing :))