Designing mechanisms isn't my forte but try this: gear all the large discs together and all the small discs separately together. The small discs are still driven by the large ones but add a clutch to disengage the two. To sync, or resynch, all gears are driven until the small gear home position is reached. When small gears are homed disengage the small gears and run 'til the large gears reach their own home position. Release the clutch and reengage the two sets of gears.
YMMV