I think displacement control is true because 1. Real experiments are displacement control 2. In load control, When the specimen fails because the force is bigger than static force, it accelerates and the simulation gets dynamic, not quasi-static.
You can define displacement constraints in different points independently.
Or you can define constraints in five points to follow U1 displacement from the sixth point and then define displacement for the sixth one.
The simulation must be displacement control and you should verify RF of the moving support v.s it's displacement. Define moving support as a rigid body and use it's Referece Point's outputs.
Regards,
M. Khodaei