another thought
a 2 part door with the front half fully supported on 2 points and hinge to the back half one support central
lay the track so the front half goes say 10mm beyond the finish position on the center line between the frame coming back to the central position as it shuts
then because the back half is centrally supported this will throw the back half 10mm towards the closed position further aided by the back section following the track sideways
in other words you will amplify the movement in a shorter space in the same way an articulated lorry has to exagirate movement to clear obstacles but in reverse
a 2 part door with the front half fully supported on 2 points and hinge to the back half one support central
lay the track so the front half goes say 10mm beyond the finish position on the center line between the frame coming back to the central position as it shuts
then because the back half is centrally supported this will throw the back half 10mm towards the closed position further aided by the back section following the track sideways
in other words you will amplify the movement in a shorter space in the same way an articulated lorry has to exagirate movement to clear obstacles but in reverse