Looking at the video, it almost seems as the rotating plates were cog wheels rotating against each other. If that were the case, your problem would be solved.
Although the encoder plates would be the geek way to do it. Just mechanically connecting them would lead to two motors doing the same job. One would force the other if you don't know exactly how much power you need to put to each of them. With the encoder plates you could have them in perfect sync. But you could also have them run in different speed, making the turtle turn.