Disabling isKinematic on a hinge joint at runtime - keeping motion to axis

It seems that, when assigning a connectedBody to a joint at runtime, setting isKinematic=false to the connected rigidbody, disrupts the position of the gameobject, causing all kinds of odd rounding errors - wiggle and chaos.

In contrast, when the hingejoint is set before, this weird rounding error doesn't seem to occur.

I've also tried setting constraints to freeze position and all but the axis along which the joint should rotate.

Is it possible to have the hinge joint behave as expected for a runtime add, i.e., allow motion only along the axis?