A servo would work, but also you can use any standard* 3 phase motor and a VFD to accomplish this. Even though you likely do not need to vary the speed, the starting and stopping current will be controlled by the VFD, which is theoretically capable of limiting the motor starting current to the FLC (Full Load Current) of the motor. At 200 ops/hour however, that is one complete cycle every 18 seconds and that means your acceleration rate will have to be relatively short, even shorter if you need controlled deceleration, i.e. braking, between cycles. That then means that you are unlikely to be able to accelerate this with a limit of motor FLC, because that would extend the ramp time. But the VFD should be able to limit the acceleration current greatly compared to any other technology, i.e. 150% or less, compared to 600%, which will reduce the de-rating necessary for the motor. For sure though, you will need to use a motor larger than the load in order to allow it to absorb the excess heat without damage. I would also recommend getting a "blown" motor, i.e. one with a separately powered cooling fan that runs continuously, not just the one attached to the motor shaft.
* Standard "inverter duty" AC motor.
If you want more help you would have to post intimate details of the actual operation, including inertia, cycle descriptions etc., which may be too proprietary. This more likely needs the personal attention of a qualified engineer who can see and study the entire process in detail, even if it means signing an NDA. But for sure this is not the sort of thing that can be "napkin engineered" by a motor or VFD salesman. There are several such independent EEs that are members of this forum who can possibly work from afar, or post your general location so they can see if they are interested in helping locally.
"Will work for salami"
