[Alan Anderson]

That's a tricky bit of hardware you have there. I'd seriously look into a way to mechanically link the two sides so they are synchronized automatically. Would there be room for a chain between them at the top, or at the bottom?

Failing a hardware solution, then encoders can work. Assuming the two sides start out in the same position, you need to "slave" one side to the other. Control one side however you want, and use its encoder value as the set point of an algorithm that controls the other side to get the other encoder to match. Since you're using lead screws, there won't be significant inertia in the system, so a simple proportional controller (drive the motor faster when it's far from target, and slower when it's close) ought to be sufficient.

I'd actually add some "feedforward" so the second motor gets some of its control from the same signal that runs the first one. That should keep them close, and the leveling control algorithm just has to account for small errors.