Axial forces do exist in motor-generators due to the magnetic center when running under load is not the same as the mechanical center when at rest. I had considered this earlier because I have experience with thrust bearings and thrust washers, having seen one pop ten feet into the air when the end plate was removed on a large electric motor! However, since you stated in the OP a condition the “power transmission is via pure torsion in a rotating drive shaft” I assumed that ruled out any consideration of an axial impulse. But, even if there is an axial impulse, we are dealing with a closed system and any internal impulse force will be met by a counter force and the COM should not move. Right? I am beginning to suspect that there may be something wrong with the question that is being asked here. It is a given, In any totally isolated system, mass is neither entering or leaving and there are no external forces acting on it, therefore there cannot be any change in the center of mass or the linear momentum due to internal forces. But what if the isolated system is started off or forced into state where the masses and forces are unbalanced? In that case, the internal forces will act to towards equilibrium and shift some mass around. In the problem under consideration, the system is isolated but it is not starting off at equilibrium. The unbalanced mass will shift from one battery to the other as it seeks equilibrium. For linear momentum and center of mass to be conserved, we are to assume that “something else” must provide for translational symmetry; finding that “something else” is the problem. My thought is, if you start or force an isolated system into an unbalanced state that requires an external force and external energy. In that case, because an external force acted on the system the COM can move as it goes towards equilibrium with no violation of conservation. There is no “something else” to be found. Once the isolated system achieves equilibrium (both batteries are equally charged) then COM will ensure there is no further shifting of the COM due to any internal forces. I wish you will provide your answer soon so I can stop thinking about this!