Applying physical restrictions to Mecanim root motion

I have a character controlled by an Animator's root motion. I'm exploring options to make the character drag ragdolls by holding them in hands. 1) Initially I've made the ragdoll's root Rigidbody kinematic and used MovePosition and MoveRotation on it to position it properly. 2) I've forcefully put the ragdoll into right position and joined it with the character using a Fixed Joint.

Unfortunately both methods lead to ragdoll glitching all around when the character's motion pushes it against a wall. I've already applied every "Ragdoll Stability" advice from the manual including enabling Projection on every joint.

A perfect solution would be a MovePosition alternative which takes in account collisions and won't move objects into walls.