Rack and pinion elevator? Can't wait to see what results!
Some random team had a rack/pinion mechanism built and working this year, only it used a beefy steel rack gear from McMaster (ouch). An early concept:
In the end, even after welding supports in for the mast, they couldn't stabilize the tower sufficiently to keep the system from twisting/binding in a few spots. Their forearm/claw attached to the elevator carrier proved too formidable for the system to handle. In the end, the night before ship, they removed the rack and pinion mast and changed to a four-bar system similar to what we used, adding a motorized wrist joint in the middle of the forearm pictured above. Quite a shock to see pics of one robot one day and then find something completely different the next! It was a good call - in the end, their arm functioned very well for them.
We have a waterjet sponsor, so I will be very interested in seeing how this application turns out for you!