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Looking at your design, you may be able to use a 200 step per revolution stepper motor using differential switching. this should give 800 steps for the revolution. When this is combined with the ratios of your worm drive it should be smooth enough drive system. All of this would still require a motor which can cope with the load required of it, and a control circuit to drive the stepper. How much torque is required to rotate the drive?
In case your wondering - I'm an office equipment technician. I have a large box of stepper motors salvaged from scrap equipment.
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