John, welcome!
Having cut several focus blocks out of microscopes, I'd highly recommend incorporating one into your rig for stacking movement. (An additional screw drive on the same axis is also helpful for rough positioning, and plenty of people use one for stacking movement--but it's hard to beat a microscope focus block for fine work).
But is the block in your Swift M3200 block a good choice? From what I'm seeing online, I don't think so. (Correct me if I'm wrong--I don't have personal experience with Swift models). The value of the scope seems appropriate for dissection--sub $200, if my quick eBay search is any guide. But if the brochure I'm looking at is correct for your model, the fine and coarse focus knobs are not coaxial. What you want is a focus block with coaxial coarse and fine knobs, with the fine adjustment running the entire length of the block's movement. Then you can use the fine control for stacking, and the coarse control for returning your rig to starting position. You can probably also remove one of the fine focus knobs and couple a motor to the rod underneath it. Many Nikon and Olympus are good candidates.
Regarding stepping motors: Since a good, off-the-shelf stepping motor can be had for something around $15--ordered to spec with the characteristics of your choice--it's hard to justify compromising much to repurpose an old one. My motor is a Kysan 1040071. It lists at $15.50 and has 0.9 degree full steps--so 400 steps per rotation. Shipping did add to that price, and it took a while--so you might check out suppliers closer to home.
Must agree with Pau that the optical arrangment you show seems very odd. Are you really shooting through both objective and eyepiece, all on extension? What happens if you place the objective alone on that extension? You might well get rather bad chromatic aberration (I don't know if Swift objectives rely on the eyepiece for correcting CA, but suspect that they do). Or it might work.
Cheers!
--Chris