It will take me a while to make a good wiring diagram. Although the diagram I posted shows the electronic and power grounds as one continuous path, actually, the negative terminal of the battery goes separately to the Sabertooth ground and to the electronic supply ground.
Taking Mike's advice, I did put 0.1 uf capacitors across the Sabertooth outputs to each of the motors and that corrected the problem. However, I then discovered something more bizarre. When the laptop AND the battery chargers are both plugged in, with the mains side in the same outlet, the motors are violently erratic.