Hinge Joints Twisting around Wrong Axis

We're simulating a piece of equipment with an articulated arm. The arm pieces are rigid bodies with colliders, connected to each other by hinge joints rotating around their X axes. We're using springs and we move the arm by changing the target angles of the hinge joint springs. The spring is set to 1e+8 with damper 0.

The problem is when the last section collides with a fixed object, pieces will twist around, definitely not limiting their movement to rotating around the X axis. When the collision is over, the pieces snap back into place.

We can't set constraints on the rigid bodies, because the arm's on a vehicle that has to move around.

Does anybody have a fix to this problem? Do configurable joints configured to act like hinge joints have the same problem?