Most of my experience with motion control is at a professional level, so I'm not sure I'd be much help with hobby components.
Might be worth using DC and a belt drive or friction clutch, then just running it into the hardstop with a time-based cutoff in the logic. Not sure how much a mini-servo could lift. Alternatively you could do a scissor-jack type deal, which would function like gearing and do a simple contact limit switch.