I think the wobbling has to do with the rotation order.
To get around it you need to use both the “Particle Replicator” Rotation as well as the “Particle Look” Rotation.
Particle Replicator Rotation
Y = thisComp.layer(“Wheel_Orientation”).transform.yRotation+90
Z = thisComp.layer(“Wheel_Orientation”).transform.orientation[2]+90
Particle Look Rotation
Y = thisComp.layer(“Wheel_Rotation”).transform.zRotation