Stepper to sequence back and forth
It definitely will work. But to not waste your time and money (engineering time is expensive) you should use stepper driver. Not just an IC, which is natural for electronics engineer, but a complete system. If it will work out and you will have to reduce costs or for whatever reason to design your own- very well, but don't let this activity to hold your own mechanical job. For stepper drivers google trinamic. They have probably all you may ever need.