I'd use claws that fully encompass the pieces. Then you can lock the gripper and move the load around.
Stepper motors are available with various torque, Nema 17 may be a bit small for your load. I also would use a DC motor or powerful servo for more torque, not a stepper. The DC motor can be powered until it stalls, with high current or some other feedback for turning it off. Torque is primarily a matter of the gear transmission ratio.