Will it work, sure anything is possible. But realize that you will only have the length of your rack of extension. Is that enough to reach the pegs you are going for? Can you source a rack long enough to do what you want to do, and still not weigh a ton, and attach the pinion to the FP gearbox?
look around on
www.howstuffworks.com and the like for examples of how a forklift, crane, elevator, etc. work this may give you more ideas, or help to refine your own.